Cut-Elimination Theorem for the Logic of Constant Domains

The logic CD is an intermediate logic (stronger than intuitionistic logic and weaker than classical logic) which exactly corresponds to the Kripke models with constant domains. It is known that the logic CD has a Gentzen-type formulation called LD (which is same as LK except that (→) and (?–) rules are replaced by the corresponding intuitionistic rules) and that the cut-elimination theorem does not hold for LD . In this paper we present a modification of LD and prove the cut-elimination theorem for it. Moreover we prove a “weak” version of cut-elimination theorem for LD , saying that all “cuts” except some special forms can be eliminated from a proof in LD . From these cut-elimination theorems we obtain some corollaries on syntactical properties of CD : fragments collapsing into intuitionistic logic. Harrop disjunction and existence properties, and a fact on the number of logical symbols in the axiom of CD . Mathematics Subject Classification : 03B55. 03F05.     

关于拟连续Domain的一个注记

证明了:(1)具有性质M的dcpo为拟连续domain当且仅当其上的下拓扑开集格在集合包含序下为连续格;(2)对于dcpo L,L为拟连续domain当且仅当ΣL的Hoare空间为局部强紧空间.     

A Square of Oppositions in Intuitionistic Logic with Strong Negation

In this paper, we introduce a Hilbert style axiomatic calculus for intutionistic logic with strong negation. This calculus is a preservative extension of intuitionistic logic, but it can express that some falsity are constructive. We show that the introduction of strong negation allows us to define a square of opposition based on quantification on possible worlds.     

关于积域上的粗糙奇异积分算子的一点注记

讨论积域上的奇异积分算子：ＴΩｆ（ｘ,ｙ） ＝ ｐ．ｖ．∫Ｒｎ×ＲｍΩ（ｕ,ｖ）｜ｕ｜ｎ｜ｖ｜ｍ ｆ（ｘ － ｕ,ｙ － ｖ）ｄｕｄｖ的Ｌｐ 有界性,及相应的Ｍａｒｃｉｎｋｉｅｗ ｉｃｚ积分的Ｌ２ 有界性． 其中Ω为类似文［４］中引进的函数类．     

A Note on the w-Global Transform of Mori Domains

Let R be a domain and let R wg be the w-global transform of R.In this note it is shown that if R is a Mori domain,then the t-dimension formula t- dim(R wg ) = t- dim(R) - 1 holds.     

A Note on Bifurcation for Harmonic Maps on Annular Domains

Mediterranean Journal of Mathematics - In this paper we consider harmonic maps u(r, θ) from an annular domain $${Omega _{rho} = B_{1}backslashbar{B}_{rho}}$$ to S 2 with the boundary...     

A Note on Property of Cauchy Integral on Classical Domains

In[1],ZhengXueanprovedthat:letRI(n×n)befirstclassicaldomain,Unbecharacteris-ticboundaryofRI,x∈Un,f(x)∈L2(Un).Asz=rx(0≤r<1)→x,Cauchyintegral∫Unf(y)det(I-zy′)-ndyconvergetoafunctioninL2(Un).Inthispaper,wewillfacusourselfonCauchyintegralofL2onclassicaldomains[2]andgetsomeproperties.Themainresultisfollowing:Theorem　LetRbeoneofclassicaldomains,LbecharacteristicboundaryofR,f∈L2(L),H(z,ξ)beCauchykernelofRandF(z)=∫Lf(u)H(z,u)u　z∈R,(1)wheretherightisLebesgueintegral;uist…     

Packing of Rounded Domains on a Sphere of Constant Curvature

Packings of congruent circles have extensively been studied as well in the Euclidean plane as on the sphere and in the hyperbolic plane. In the present paper packings of more general domains are considered and the proof of a long claimed result of the author is given.     

A Note on Homogenization of Parabolic Equation in Perforated Domains

We are concerned with a class of parabolic equations in periodically perforated domains with a homogeneous Neumann condition on the boundary of holes.By using the periodic unfolding method in perforated domains, we obtain the homogenization results under the conditions slightly weaker than those in the corresponding case considered by Nandakumaran and Rajesh(Nandakumaran A K, Rajesh M. Homogenization of a parabolic equation in perforated domain with Neumann boundary condition. Proc. Indian Acad. Sci.(Math. Sci.), 2002, 112(1): 195–207). Moreover,these results generalize those obtained by Donato and Nabil(Donato P, Nabil A. Homogenization and correctors for the heat equation in perforated domains. Ricerche di Matematica L. 2001, 50: 115–144).     

A Note on Doubly Connected Surfaces of Constant Mean Curvature with Prescribed Boundary

In this paper we prove the existence of a constant mean curvature surface spanning two given convex curves in parallel planes of ℝ³ under hypotheses relating the distance between the planes, the curvature of the curves and the mean curvature. It is also proved that the surface is a radial graph over a unit sphere.This author was partially Supported by Fapergs. Mathematics Subject Classifications (2000): 53A10, 53C42, 35J60     

A Note on the Joint Replenishment Problem under Constant Demand

This note considers the joint replenishment inventory problem for N items under constant demand. The frequently-used cyclic strategy (T; k₁, …, k _N ) is investigated: a family replenishment is made every T time units and item i is included in each k _i th replenishment. Goyal proposed a solution to find the global optimum within the class of cyclic strategies. However, we will show that the algorithm of Goyal does not always lead to the optimal cyclic strategy. A simple correction is suggested.     

A Note on Lp Boundedness for Maximal Singular Integrals on Product Domains

§ 1.ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＳｔａｔｅｍｅｎｔｓｏｆＲｅｓｕｌｔｓ　Ｉｔｉｓｗｅｌｌ ｋｎｏｗｎｔｈａｔｔｈｅｍａｘｉｍａｌｓｉｎｇｕｌａｒｉｎｔｅｇｒａｌｏｎｐｒｏｄｕｃｔｄｏｍａｉｎｓｉｓｖｅｒｙｕｓｅｆｕｌｌｉｎｈａｒｍｏｎｉｃａｎａｌｙｓｉｓ.Ｈｅｒｅｗｅｌｉｓｔｔｗｏｒｅｓｕｌｔｓｒｅｌａｔｅｄｔｏｔｈｉｓｐａｐｅｒ.Ｓｅｅ [1 ] ,[2 ]ａｎｄｔｈｅｒｅｆｅｒｅｎｃｅｓｔｈｅｒｅｉｎ .　Ｆｒｏｍ [1 ] ,ｗｅｋｎｏｗｔｈｅｆｏｌｌｏｗｉｎｇｆａｃｔ.　ＳｕｐｐｏｓｅｔｈａｔＫ(ｘ,ｙ)ｉｓｌ…     

平面常宽凸域的不对称性度量

通过引入刻画平面常宽凸域的不对称性函数,证明了在平面常宽凸域中,圆域 是最对称的,而Reuleaux三角形是最不对称的．     

关于二阶常系数线性齐次常微分方程的通解的一个注记

文献[1]给出了二阶常系数线性齐次常微分方程的通解形式,但未回答除了通解形式的解是否还有其它形式的解,本文指出通解包含了所有的解,并给出一个只需要高等数学知识的证明.     

A Note on Boundary Unique Contination for Harmonic Functions in Non-Smooth Domains

In this note, we prove the boundary unique continuation property for harmonic function dfined on convex domain     

Specialization of Loop Rules of a Sequent Calculus of Intuitionistic Temporal Logic with Time Gaps

The paper deals with the loop-rule problem in the first-order intuitionistic temporal logic sequent calculus LBJ. The calculus LBJT is intended for the specialization of the antecedent implication rule. The invertibility of some of the LBJT rules and the syntactic admissibility of the structural rules and the cut rule in LBJT, as well as the equivalence of LBJ and LBJT, are proved. The calculus LBJT2 is intended for the specialization of the antecedent universal quantifier and antecedent box rules. The decidability of LBJT2 is proved.