Rocky coast processes: with special reference to the recession of soft rock cliffs

Substantial progress in research on the recession of coastal cliffs composed of soft materials has been made in recent years and data with higher accuracy have been accumulated. This paper provides the state of the art review in the recession studies and highlights two new findings obtained from the reanalysis of existing data. The review topics are: episodic and localized nature of cliff recession; the development of cliffline; the relationship between cliff height and recession rate; mechanisms of cliff toe erosion by waves; a fundamental equation for wave-induced toe erosion; factors controlling toe erosion; and slope instabilities and mass movements. The findings are presented on (1) the temporal change in cliffline recession mode and (2) the effect of beach sediment at the cliff base on the cliff erosion.     

半无限二次规划

本文给出了半无限二次规划和它的对偶规划之间没有间隙的条件。还证明了具有对偶间隙的半无限二次规划可以通过扰动其目标函数来消除,且扰动后的半无限二次规划的最优值收敛于原始半无限二次规划的最优值。     

Upper-semi-continuity and cone-concavity of multi-valued vector functions in a duality theory for vector optimization

Following a few words on multifunctions in the mathematical literature, a very brief recall on dual spaces, some preliminary notations and definitions in the introduction, we give some results on those functions in the second paragraph. In the third paragraph, a duality theory in cone-optimization involving multifunctions is developed with the concept of the strong instead of the weak cone-optimality criterium. The results so obtained account for existing ones on univocal vector-function optimization and they hold in spaces of arbitrary dimension.The author is grateful to the refuree's helpful suggestions.     

Cover and Bounded Parallel Faces

We use the cover or the closure of the cover in order to determine when two disjoint closed convex sets have parallel faces, one of them being bounded. Moreover, we show that the study of the closure of the cover gives interesting results about the cover itself.     

On a Class of Convex Sets and Functions

Given a convex subset C of ⁿ, the set-valued mapping C (where 0C is, by convention, the recession cone of C) is increasing on ₊ if and only if C contains the origin, and decreasing on ₊ if and only if C is contained in its recession cone. This simple fact enables us to define a binary operation which combines a concave or convex function on ^m with a convex subset of ⁿ to produce a convex subset of ^n+m. This binary operation is the set theoretic counterpart of a functional operation introduced by the author. In this paper, we present a detailed study of the class of convex subsets which are contained in their recession cones, and we establish some remarkable properties of our binary operation.Mathematics Subject Classifications (2000) 26A51, 26B25, 26E25.     

环境恶化与经济衰退的动力学模型

建立了环境经济耦合系统的动力学模型,分析了环境污染引发经济衰退的机制.结果表明:环境恶化和相应的经济损失可能导致经济衰退,并且由于环境系统演化的非线性,在某些情况下,经济衰退可能是难以逆转的.如果进行适当的污染治理投资,则可能改善环境状况,从而避免经济衰退.     

Relations between the convexity of a set and the differentiability of its support function

It is known that, in finite dimensions, the support function of a compact convex set with nonempty interior is differentiable excepting the origin if and only if the set is strictly convex. In this paper, we realize a thorough study of the relations between the differentiability of the support function on the interior of its domain and the convexity of the set, mainly for unbounded sets. Then, we revisit some results related to the differentiability of the cost function associated to a production function.     

Exact recession velocity and cosmic redshift based on cosmological principle and Yang-Mills gravity

Based on the cosmological principle and quantum Yang-Mills gravity in the super-macroscopic limit, we obtain an exact recession velocity and cosmic redshift z, as measured in an inertial frame F ≡ F(t, x, y, z). For a matter-dominated universe, we have the effective cosmic metric tensor G_(μν)(t) =(B~2(t),-A~2(t),-A~2(t),-A~2(t)),A ∝ B ∝ t~(1/2), where t has the operational meaning of time in F frame. We assume a cosmic action S ≡ S cos involving Gμν(t) and derive the ‘Okubo equation' of motion, G μν(t)?μS ?νS-m2= 0, for a distant galaxy with mass m. This cos-√mic equation predicts an exact recession velocity, ■, where H = A˙(t)/A(t) and Co = B/A, as observed in the inertial frame F. For small velocities, we have the usual Hubble's law r≈ rH for recession velocities. Following the formulation of the accelerated Wu-Doppler effect, we investigate cosmic redshifts z as measured in F. It is natural to assume the massless Okubo equation, G μν(t)?μψe?νψe= 0, for light emitted from accelerated distant galaxies. Based on the principle of limiting continuation of physical laws, we obtain a transformation for covariant wave 4-vectors between and inertial and an accelerated frame, and predict a relationship for the exact recession velocity and cosmic redshift, z = [(1 + V_r)/(1-V_r~2)~(1/2)]-1, where Vr= r˙/Co 1, as observed in the inertial frame F. These predictions of the cosmic model are consistent with experiments for small velocities and should be further tested.     

十七世纪意大利经济衰落的原因探析

意大利地区是世界近代史上最早出现资本主义萌芽的地区之一。到十七世纪,意大利进入经济结构调整期。纺织业的衰落、农业艰难的复兴、城乡经济的对立以及人口增长缓慢使意大利的近代化进程落后于同时期的西欧诸国,进而使其丧失了地中海贸易的中心地位。