Post's Problem for Reducibilities of Bounded Complexity

In this paper we consider the we known method by E. Post of solving the problem of construction of recursively enumerable sets that have a degree intermediate between the degrees of recursive and complete sets with respect to a given reducibility. Post considered reducibilities ≤_m, ≤_btt, ≤_tt and ≤_T and solved the problem for al of them except ≤_T. Here we extend Post's original method of construction of incomplete sets onto two wide classes of sub‐Turing reducibilities what were studying in [1, 2].     

Abelian Logic and the Logics of Pointed Lattice-Ordered Varieties

We consider the class of pointed varieties of algebras having a lattice term reduct and we show that each such variety gives rise in a natural way, and according to a regular pattern, to at least three interesting logics. Although the mentioned class includes several logically and algebraically significant examples (e.g. Boolean algebras, MV algebras, Boolean algebras with operators, residuated lattices and their subvarieties, algebras from quantum logic or from depth relevant logic), we consider here in greater detail Abelian ℓ-groups, where such logics respectively correspond to: i) Meyer and Slaney’s Abelian logic [31]; ii) Galli et al.’s logic of equilibrium [21]; iii) a new logic of “preservation of truth degrees”. This paper was written while the second author was a Visiting Professor in the Department of Education at the University of Cagliari. The facilities and assistance provided by the University and by the Department are gratefully acknowledged.     

Algebraization of the Three‐valued BCK‐logic

In this paper a definition of n‐valued system in the context of the algebraizable logics is proposed. We define and study the variety V₃, showing that it is definitionally equivalent to the equivalent quasivariety semantics for the “Three‐valued BCK‐logic”. As a consequence we find an axiomatic definition of the above system.     

向量值Nevanlinna第二基本定理的余项S(r)的估计

首先通过建立并证明推广的对数导数基本引理,讨论了１２π∫２π０ｌｏｇ＋‖ｆ′（ｒｅｉθ）‖‖ｆ（ｒｅｉθ）‖ｄθ的增长问题,进而对向量值Ｎｅｖａｎｌｉｎｎａ第二基本定理的余项进行了估计     

多供应商条件下选址模型的一个研究结果

通过实例和对模型的分析,得出[1]中已有多供应商条件上所建模型的不合理性,并提出了模型合理性的原则。     

The Law of the Iterated Logarithm for Weakly Dependent Hilbert Space Valued Random Variables

We consider the bounded and compact laws of the iterated logarithm for weakly dependent Hilbert space valued random variables. Under optimal moment conditions, we prove the bounded and compact laws of the iterated logarithm for sequences of identically distributed Hilbert space valued random variables satisfying the uniform strong mixing condition.     

The lattice of extensions of the minimal logic

In this article, we survey the results on the lattice of extensions of the minimal logic Lj, a paraconsistent analog of the intuitionistic logic Li. Unlike the well-studied classes of explosive logics, the class of extensions of the minimal logic has an interesting global structure. This class decomposes into the disjoint union of the class Int of intermediate logics, the class Neg of negative logics with a degenerate negation, and the class Par of properly paraconsistent extensions of the minimal logic. The classes Int and Neg are well studied, whereas the study of Par can be reduced to some extent to the classes Int and Neg.     

Boolos‐style proofs of limitative theorems

Boolos's proof of incompleteness is extended straightforwardly to yield simple “diagonalization‐free” proofs of some classical limitative theorems of logic. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Complete Convergence of Moving Average Process with Banach Space Valued Random Elements

Let {Y _i ;−∞<i<∞} be a doubly infinite sequence of independent random elements taking values in a separable real Banach space and stochastically dominated by a random variable X. Let {a _i ;−∞<i<∞} be an absolutely summable sequence of real numbers and set V _i =∑ _k=−∞^∞ a _i+k Y _i ,i≥1. In this paper, we derive that if and E|X| ^μ log  ^ρ |X|<0, for some μ (0<μ<2, μ≠1) and ρ>0 then for all ε>0. This work was partially supported by the Korean Research Foundation Grant funded by the Korean Government (KRF-2006-353-C00006, KRF-2006-251-C00026).     

多元函数中值定理中介值的渐近性

讨论了n元函数中值定理中介值的渐近性质.     

两指标B值鞅的A.S.收敛性与B空间的Radon-Nikodym性

本文证明了在F4条件下，任一Llog+L有界的两指标B值鞅几乎处处收敛到一可积的B值随机变量当且仅当B空间有Radon-Nikodym性质．进一步还证明了在更弱的局部F4条件下，上述结论也成立．     

Sequent Calculi with Analytic Cut for Logics of Time and Knowledge with Perfect Recall

In this paper, we consider two logics of time and knowledge. These logics involve the discrete time linear temporal logic operators ``next' and ``until'. In addition, they contain an indexed set of unary epistemic modalities ``agent $i$ knows'. In these logics, the temporal and epistemic dimensions may interact. The particular interactions we consider capture perfect recall. We consider perfect recall in synchronously distributed systems and in systems without any assumptions. For these logics, we present sequent calculi with an analytic cut rule. Thus, we get proof systems where proof-search becomes decidable. The soundness and completeness of these calculi are proved.     

Representations of MV‐algebras by sheaves

In this paper, inspired by methods of Bigard, Keimel, and Wolfenstein ([2]), we develop an approach to sheaf representations of MV‐algebras which combines two techniques for the representation of MV‐algebras devised by Filipoiu and Georgescu ([18]) and by Dubuc and Poveda ([16]). Following Davey approach ([12]), we use a subdirect representation of MV‐algebras that is based on local MV‐algebras. This allowed us to obtain: (a) a representation of any MV‐algebras as MV‐algebra of all global sections of a sheaf of local MV‐algebras on the spectruum of its prime ideals; (b) a representation of MV‐algebras, having the space of minimal prime ideals compact, as MV‐algebra of all global sections of a Hausdorff sheaf of MV‐chains on the space of minimal prime ideals, which is a Stone space; (c) an adjunction between the category of all MV‐algebras and the category of MV‐algebraic spaces, where an MV‐algebraic space is a pair (X, F), where X is a compact topological space and F is a sheaf of MV‐algebras with stalks that are local (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Finite Model Property of Intuitionistic Modal Logics over MIPC

MIPC is a well-known intuitionistic modal logic of Prior (1957) and Bull (1966). It is shown that every normal intuitionistic modal logic L over MIPC has the finite model property whenever L is Kripke-complete and universal.     

On the structure of certain valued fields

In this article, we study the structure of finitely ramified mixed characteristic valued fields. For any two complete discrete valued fields $K_1$ and $K_2$ of mixed characteristic with perfect residue fields, we show that if the n-th residue rings are isomorphic for each $n\ge 1$, then $K_1$ and $K_2$ are isometric and isomorphic. More generally, for $n_1\ge 1$, there is $n_2$ depending only on the ramification indices of $K_1$ and $K_2$ such that any homomorphism from the $n_1$-th residue ring of $K_1$ to the $n_2$-th residue ring of $K_2$ can be lifted to a homomorphism between the valuation rings. Moreover, we get a functor from the category of certain principal Artinian local rings of length n to the category of certain complete discrete valuation rings of mixed characteristic with perfect residue fields, which naturally generalizes the functorial property of unramified complete discrete valuation rings. Our lifting result improves Basarab's relative completeness theorem for finitely ramified henselian valued fields, which solves a question posed by Basarab, in the case of perfect residue fields.     

An extension of Asgeirsson's mean value theorem for solutions of the ultra-hyperbolic equation in dimension four

In 1937 Asgeirsson established a mean value property for solutions of the general ultra-hyperbolic equation in 2n variables. In the case of four variables, it states that the integrals of a solution over certain pairs of conjugate circles are the same. In this paper we extend this result to non-degenerate conjugate conics, which include the original case of conjugate circles and adds the new case of conjugate hyperbolae.The broader context of this result is the geometrization of Fritz John's 1938 analysis of the ultra-hyperbolic equation. Solutions of the equation arise as the condition for functions on line space to come from line integrals of functions in Euclidean 3-space, and hence it appears as a compatibility condition for tomographic data.The introduction of the canonical neutral Kaehler metric on the space of oriented lines clarifies the relationship and broadens the paradigm to allow new insights. In particular, it is proven that a solution of the ultra-hyperbolic equation has the mean value property over any pair of curves that arise as the image of John's conjugate circles under a conformal map. These pairs of curves are then shown to be conjugate conics, which include circles and hyperbolae.John identified conjugate circles with the two rulings of a hyperboloid of 1-sheet. Conjugate hyperbolae are identified with the two rulings of either a piece of a hyperboloid of 1-sheet or a hyperbolic paraboloid.     

Infinitely Many Critical Points of Non-Differentiable Functions and Applications to a Neumann-Type Problem Involving the p-Laplacian

For a family of functionals in a Banach space, which are possibly non-smooth and depend also on a positive real parameter, the existence of a sequence of critical points (according to Motreanu and Panagiotopoulos (“Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities,” Nonconvex Optimization Applications, Vol. 29, Kluwer, Dordrecht, 1998, Chap. 3)) is established by mainly adapting a new technique due to Ricceri (2000, J. Comput. Appl. Math.113, 401-410). Two applications are then presented. Both of them treat the Neumann problem for an elliptic variational-hemivariational inequality with p-Laplacian.