bluuebunny/crossref_metadata_2025_split huggingface dataset:
The Operators of Vector Logic
Authors: Mizraji Eduardo 
Published: May 2007

AbstractVector logic is a mathematical model of the propositional calculus in which the logical variables are represented by vectors and the logical operations by matrices. In this framework, many tautologies of classical logic are intrinsic identities between operators and, consequently, they are valid beyond the bivalued domain. The operators can be expressed as Kronecker polynomials. These polynomials allow us to show that many important tautologies of classical logic are generated from basic operators via the operations called Type I and Type II products. Finally, it is described a matrix version of the Fredkin gate that extends its properties to the many‐valued domain, and it is proved that the filtered Fredkin operators are second degree Kronecker polynomials that cannot be generated by Type I or Type II products.Mathematics Subject Classification: 03B05, 03B50.
Decidability of ∀*∀‐Sentences in Membership Theories
Authors: Omodeo Eugenio G. , Parlamento Franco , Policriti Alberto 
Published: May 2007

AbstractThe problem is addressed of establishing the satisfiability of prenex formulas involving a single universal quantifier, in diversified axiomatic set theories. A rather general decision method for solving this problem is illustrated through the treatment of membership theories of increasing strength, ending with a subtheory of Zermelo‐Fraenkel which is already complete with respect to the ∀*∀ class of sentences. NP‐hardness and NP‐completeness results concerning the problems under study are achieved and a technique for restricting the universal quantifier is presented.Mathematics Subject Classification: 03B25, 03E30.
The Recursively Mahlo Property in Second Order Arithmetic
Authors: Rathjen Michael 
Published: May 2007

AbstractThe paper characterizes the second order arithmetic theorems of a set theory that features a recursively Mahlo universe; thereby complementing prior proof‐theoretic investigations on this notion. It is shown that the property of being recursively Mahlo corresponds to a certain kind of β‐model reflection in second order arithmetic. Further, this leads to a characterization of the reals recursively computable in the superjump functional.Mathematics Subject Classification: 03F35, 03F15, 03E70.
Remarks on Uniformly Finitely Precomplete Positive Equivalences
Authors: Yu. Shavrukov V. 
Published: May 2007

AbstractThe paper contains some observations on e‐complete, precomplete, and uniformly finitely precomplete r. e. equivalence relations. Among these are a construction of a uniformly finitely precomplete r. e. equivalence which is neither e‐ nor precomplete, an extension of Lachlan's theorem that all precomplete r. e. equivalences are isomorphic, and a characterization of sets of fixed points of endomorphisms of uniformly finitely precomplete r. e. equivalences.Mathematics Subject Classification: 03D45.
Inconsistency of GPK + AFA
Authors: Esser Olivier 
Published: May 2007

AbstractM. Forti and F. Honsell showed in [4] that the hyperuniverses defined in [2] satisfy the anti‐foundation axiom X1 introduced in [3]. So it is interesting to study the axiom AFA, which is equivalent to X1 in ZF, introduced by P. Aczel in [1]. We show in this paper that AFA is inconsistent with the theory GPK. This theory, which is first order, is defined by E. Weydert in [6] and later by M. Forti and R. Hinnion in [2]. It includes all general hyperuniverses as defined in [5]. In order to achieve our aim, we need to define ordinals in GPK and to study some of their properties.Mathematics Subject Classification: 03E70, 03E10.
A Note on Closed Degrees of Difficulty of the Medvedev Lattice
Authors: Bianchini Caterina , Sorbi Andrea 
Published: May 2007

AbstractWe consider some nonprincipal filters of the Medvedev lattice. We prove that the filter generated by the nonzero closed degrees of difficulty is not principal and we compare this filter, with respect to inclusion, with some other filters of the lattice. All the filters considered in this paper are disjoint from the prime ideal generated by the dense degrees of difficulty.Mathematics Subject Classification: 03D30.
Analyse de complexité pour un théorème de Hall sur les fractions continues
Authors: Labhalla Salah , Lombardi Henri 
Published: May 2007

AbstractWe give a polynomial time controlled version of a theorem of M. Hall: every real number can be written as the sum of two irrational numbers whose developments into a continued fraction contain only 1, 2, 3 or 4.Mathematics Subject Classification: 03D15, 03F60, 11A55, 68Q25.
Tense Logic Without Tense Operators
Authors: Wolter Frank 
Published: May 2007

AbstractWe shall describe the set of strongly meet irreducible logics in the lattice ϵLin.t of normal tense logics (in the bimodal propositional language) of weak orderings. Based on this description it is shown that all logics in ϵLin.t are independently axiomatizable. Then the description is used in order to investigate tense logics with respect to decidability, finite axiomatizability, axiomatization problems and completeness with respect to Kripke semantics. The main tool for the investigation is a translation of bimodal formulas into a language talking about partitions of general frames into intervals so that relative to both Kripke frames and descriptive frames the expressive power of both languages coincides.Mathematics Subject Classification: 03B45, 03B25.
A Note on Boolean Algebras with Few Partitions Modulo some Filter
Authors: Huberich Markus 
Published: May 2007

AbstractWe show that for every uncountable regular κ and every κ‐complete Boolean algebra B of density ≤ κ there is a filter F ⊆ B such that the number of partitions of length < modulo κF is ≤2<κ. We apply this to Boolean algebras of the form P(X)/I, where I is a κ‐complete κ‐dense ideal on X.Mathematics Subject Classification: 06E05, 03C20.
Modal Aggregation and the Theory of Paraconsistent Filters
Authors: Apostoli Peter 
Published: May 2007

AbstractThis paper articulates the structure of a two species of weakly aggregative necessity in a common idiom, neighbourhood semantics, using the notion of a k‐filter of propositions. A k‐filter on a non‐empty set I is a collection of subsets of I which (i) contains I, (ii) is closed under supersets on I, and (iii) contains ∪{Xi ≤ Xj : 0 ≤ i < j ≤ k} whenever it contains the subsets X0,…, Xk. The mathematical content of the proof that weakly aggregative modal logic is complete relative to k‐ary frame theory, the standard semantic idiom for weakly aggregative modal logic (see [1]) is presented in language‐independent terms as a representation theorem for k‐filters: every non‐trivial k‐filter is included in the union of ≤ k non‐trivial filters. The elementary theory of k‐filters is developed and then applied in the form of an ultrafilter extension result for k‐ary frame theory.Mathematics Subject Classification: 03B45.
Modal Tree‐Sequents
Authors: Cerrato Claudio 
Published: May 2007

AbstractWe develop cut‐free calculi of sequents for normal modal logics by using treesequents, which are trees of sequences of formulas. We introduce modal operators corresponding to the ways we move formulas along the branches of such trees, only considering fixed distance movements. Finally, we exhibit syntactic cut‐elimination theorems for all the main normal modal logics.Mathematics Subject Classification: 03B45, 03F05.
A Cardinal Pattern Inspired by AD
Authors: Apter Arthur W. 
Published: May 2007

AbstractAssuming Con(AD), a model in which there are unboundedly many regular cardinals below Θ and in which the only regular cardinals below Θ are limit cardinals was previously constructed. Using a large cardinal hypothesis far beyond Con(AD), we construct in this paper a model in which there is a proper class of regular cardinals and in which the only regular cardinals in the universe are limit cardinals.Mathematics Subject Classification: 03E55, 03E60.
Polymodal Lattices and Polymodal Logic
Authors: Bell John L. 
Published: May 2007

AbstractA polymodal lattice is a distributive lattice carrying an n‐place operator preserving top elements and certain finite meets. After exploring some of the basic properties of such structures, we investigate their freely generated instances and apply the results to the corresponding logical systems — polymodal logics — which constitute natural generalizations of the usual systems of modal logic familiar from the literature. We conclude by formulating an extension of Kripke semantics to classical polymodal logic and proving soundness and completeness theorems.Mathematics Subject Classification: 03G10, 06D99, 03B45.
The Maximal Closed Classes of Unary Functions in p‐Valued Logic
Authors: Renren Liu , Czukai Lo 
Published: May 2007

AbstractIn many‐valued logic the decision of functional completeness is a basic and important problem, and the thorough solution to this problem depends on determining all maximal closed sets in the set of many‐valued logic functions. It includes three famous problems, i.e., to determine all maximal closed sets in the set of the total, of the partial and of the unary many‐valued logic functions, respectively. The first two problems have been completely solved ([1], [2], [8]), and the solution to the third problem boils down to determining all maximal subgroups in the k‐degree symmetric group Sk, which is an open problem in the finite group theory. In this paper, all maximal closed sets in the set of unary p‐valued logic functions are determined, where p is a prime.Mathematics Subject Classification: 03B50, 20B35.
Effectively and Noneffectively Nowhere Simple Sets
Authors: Harizanov Valentina S. 
Published: May 2007

AbstractR. Shore proved that every recursively enumerable (r. e.) set can be split into two (disjoint) nowhere simple sets. Splitting theorems play an important role in recursion theory since they provide information about the lattice ϵ of all r. e. sets. Nowhere simple sets were further studied by D. Miller and J. Remmel, and we generalize some of their results. We characterize r. e. sets which can be split into two (non) effectively nowhere simple sets, and r. e. sets which can be split into two r. e. non‐nowhere simple sets. We show that every r. e. set is either the disjoint union of two effectively nowhere simple sets or two noneffectively nowhere simple sets. We characterize r. e. sets whose every nontrivial splitting is into nowhere simple sets, and r. e. sets whose every nontrivial splitting is into effectively nowhere simple sets. R. Shore proved that for every effectively nowhere simple set A, the lattice L* (A) is effectively isomorphic to ϵ*, and that there is a nowhere simple set A such that L*(A) is not effectively isomorphic to ϵ*. We prove that every nonzero r. e. Turing degree contains a noneffectively nowhere simple set A with the lattice L*(A) effectively isomorphic to ϵ*.Mathematics Subject Classification: 03D25, 03D10.
Splittings of 0' into the Recursively Enumerable Degrees
Authors: Yi Xiaoding 
Published: May 2007

AbstractLachlan [9] proved that there exists a non‐recursive recursively enumerable (r. e.) degree such that every non‐recursive r. e. degree below it bounds a minimal pair. In this paper we first prove the dual of this fact. Second, we answer a question of Jockusch by showing that there exists a pair of incomplete r. e. degrees a0, a1 such that for every non‐recursive r. e. degree w, there is a pair of incomparable r. e. degrees b0, b2 such that w = b0 V b1 and bi for i = 0, 1.Mathematics Subject Classification: 03D25, 03D30.
Precovers, Modalities and Universal Closure Operators in a Topos
Authors: Bell John L. , Gebellato Silvia 
Published: May 2007

AbstractIn this paper we develop the notion of formal precover in a topos by defining a relation between elements and sets in a local set theory. We show that such relations are equivalent to modalities and to universal closure operators. Finally we prove that these relations are well characterized by a convenient restriction to a particular set.Mathematics Subject Classification: 03G30, 03B20, 03F55.
Decidability in Intuitionistic Type Theory is Functionally Decidable
Authors: Valentini Silvio 
Published: May 2007

AbstractIn this paper we show that the usual intuitionistic characterization of the decidability of the propositional function B(x) prop [x : A], i. e. to require that the predicate (∀x ∈ A) (B(x) ∨ ¬ B(x)) is provable, is equivalent, when working within the framework of Martin‐Löf's Intuitionistic Type Theory, to require that there exists a decision function ψ: A → Boole such that (∀x ∈ A) ((ψ(x) = Boole true) ↔ B(x)). Since we will also show that the proposition x = Boole true [x: Boole] is decidable, we can alternatively say that the main result of this paper is a proof that the decidability of the predicate B(x) prop [x : A] can be effectively reduced by a function ψ A → Boole to the decidability of the predicate ψ(x) = Boole true [x : A]. All the proofs are carried out within the Intuitionistic Type Theory and hence the decision function ψ, together with a proof of its correctness, is effectively constructed as a function of the proof of (∀x ∈ A)(B(x) ∨ ¬ B(x)).Mathematics Subject Classification: 03B15, 03B20.
The Computation of Partial Recursive Word‐Functions Without Read Instructions
Authors: Petersen Holger 
Published: May 2007

AbstractIn this note we consider register‐machines with symbol manipulation capabilities. They can form words over a given alphabet in their registers by appending symbols to the strings already stored. These machines are similar to Post's normal systems and the related machine‐models discussed in the literature. But unlike the latter devices they are deterministic and are not allowed to read symbols from the front of the registers. Instead they can compare registers and erase them. At first glance it is surprising that in general these devices are as powerful as the seemingly stronger models. Here we investigate the borderline of universality for these machines.Mathematics Subject Classification: 03D20, 68Q05, 68Q10.
The Axiom of Choice in Quantum Theory
Authors: Brunner Norbert , Svozil Karl , Baaz Matthias 
Published: May 2007

AbstractWe construct peculiar Hilbert spaces from counterexamples to the axiom of choice. We identify the intrinsically effective Hamiltonians with those observables of quantum theory which may coexist with such spaces. Here a self adjoint operator is intrinsically effective if and only if the Schrödinger equation of its generated semigroup is soluble by means of eigenfunction series expansions.Mathematics Subject Classification: 03E35, 81P10, 03E25, 35Q40, 46B26, 47A60.
Expanding the phenotype of fragile X‐associated tremor/ataxia syndrome: A new female case
Authors: Horvath Judit , Morris Michael , Bottani Armand , Moix Isabelle , Delavelle Jacqueline , Burkhard Pierre R. 
Published: May 2007

AbstractWe report an original case of fragile X‐associated tremor/ataxia syndrome in a female carrier, who had been misdiagnosed for years because of unusual features mimicking other movement or cerebrovascular disorders. She exhibited features that have not been previously described, including voice and head tremor as well as spasmodic laryngeal dystonia. Brain MRI showed widespread leukoencephalopathy reminiscent of vascular encephalopathy, exemplifying the diversity of MRI abnormalities that could be associated with the condition. © 2007 Movement Disorder Society
Skin cancers and precancerous lesions in Parkinson's disease patients
Authors: Ferreira Joaquim , Silva João Maia , Freire Rita , Pignatelli João , Guedes Leonor Correia , Feijó Alexandra , Rosa Mário Miguel , Coelho Miguel , Costa João , Noronha Ana , Hewett Russell , Gomes A. Marques , de Castro J.L. Cirne , Rascol Olivier , Sampaio Cristina 
Published: May 2007

AbstractOur objective was to evaluate the frequency of neoplastic and preneoplastic skin lesions in Parkinson's disease (PD) patients when compared with an aged‐matched population. We performed a cross‐sectional survey in PD patients and in an age‐matched control group. Patients and controls were examined by a movement disorder specialist and a dermatologist. 150 PD patients and 146 controls were included. Thirty‐five PD patients (23.3%) presented skin lesions that could be classified as neoplastic or preneoplastic vs. 20 subjects in the control group (13.7%) (OR 95%, CI 1.92 [1.05, 3.51]). However, this difference lost statistical significance when adjusted for gender (recruitment of controls was matched just for age with an over representation of males in the PD group). Twenty‐nine PD patients (19%) presented actinic keratosis and basal cell carcinoma was diagnosed in 4 patients (3%). Although nonconclusive, our results are in agreement with previous studies suggesting an increased risk of skin cancer in PD patients. The frequency of actinic keratosis in PD patients and the associated risk to develop melanoma recommends its screening in future epidemiological studies. © 2007 Movement Disorder Society
Impaired cardiovascular autonomic function in Parkinson's disease with visual hallucinations
Authors: Oka Hisayoshi , Yoshioka Masayuki , Onouchi Kenji , Morita Masayo , Mochio Soichiro , Suzuki Masahiko , Hirai Toshiaki , Urashima Mitsuyoshi , Inoue Kiyoharu 
Published: May 2007

AbstractWe assessed the relations of visual hallucinations (VH) to cardiovascular autonomic dysfunction in patients with Parkinson's disease (PD). The subjects were 37 patients without VH (VH(−)) and 31 with VH (VH(+)). Autonomic function was evaluated on the basis of cardiac 123‐radioiodinated metaiodobenzylguanidine (123I‐MIBG) uptake and hemodynamic testing with Valsalva maneuver. Systolic blood pressure (SBP) and plasma norepinephrine concentrations (NE) were measured by tilt‐table testing. 123I‐MIBG uptake was lower in VH(+) than VH(−). Hemodynamic studies showed that VH(−) had only cardiac sympathetic and parasympathetic dysfunction, while VH(+) additionally had reduced vasomotor sympathetic functions. The fall in SBP during tilt‐table testing was greater in VH(+) than VH(−). NE and its difference in the supine and upright positions were decreased in VH(+). We conclude that cardiac and vasomotor sympathetic dysfunction is more severe in VH(+) than in VH(−). Severe dysfunction in PD with VH is probably attributed to Lewy‐body lesions or neuronal loss in sympathetic ganglia, the central autonomic system, or both. © 2007 Movement Disorder Society
A stable energy‐conserving approach for frictional contact problems based on quadrature formulas
Authors: Hager C. , Hüeber S. , Wohlmuth B. I. 
Published: May 2007

AbstractA common approach for the numerical simulation of non‐linear multi‐body contact problems is the use of Lagrange multipliers to model the contact conditions. The stability of standard algorithms is improved by introducing a modified mass matrix which assigns no mass to the potential contact nodes. By this, the spurious algorithmic oscillations in the multiplier do not occur any more, which facilitates the application of the primal–dual active set strategy to dynamical contact problems. The new mass matrix is calculated via a modified quadrature formula that needs no extra computational cost. In addition the conservation properties of the underlying algorithm are transferred to the modified mass version. Different numerical examples for frictional two‐body contact problems illustrate the improvement in the results for the contact stresses. Copyright © 2007 John Wiley & Sons, Ltd.
Dynamic selective pressure using hybrid evolutionary and ant system strategies for structural optimization
Authors: Kaveh A. , Shahrouzi M. 
Published: May 2007

AbstractGenetic algorithms have already been applied to various fields of engineering problems as a general optimization tool in charge of expensive sampling of the coded design space. In order to reduce such a computational cost in practice, application of evolutionary strategies is growing rapidly in the adaptive use of problem‐specific information. This paper proposes a hybrid strategy to utilize a cooperative dynamic memory of more competitive solutions combining indirect information share in ant systems with direct constructive genetic search. Some proper coding techniques are employed to enable testing the method with various sets of control parameters. As a challenging field of interest, its application to structural layout optimization is considered while an example of a traveling salesman problem is also treated as a combinatorial benchmark. Copyright © 2007 John Wiley & Sons, Ltd.
Current approaches for risk stratification of infectious complications in pediatric oncology
Authors: Härtel Christoph , Deuster Maresa , Lehrnbecher Thomas , Schultz Christian 
Published: May 2007

AbstractInfections are serious complications of cytoreductive therapy in pediatric cancer patients presenting with febrile neutropenia. It is standard of care to initiate empirical intravenous broad‐spectrum antibiotics until the fever and neutropenia resolve. However, it might be effective and safe to allow for early hospital discharge in certain subgroups of patients. Two strategies for risk stratification of pediatric cancer patients with regard to infectious complications are discussed in this review: (1) clinical risk parameters and laboratory measures to assist therapeutic management at presentation with fever in neutropenia, and (2) investigations of individual genetic susceptibility factors to tailor potential prophylactic approaches. Given the data available from a significant number of small studies, a large prospective non‐inferiority trial is essential to assess low‐risk clinical factors and additional laboratory or genetic markers for their predictive value. Pediatr Blood Cancer 2007;49:767–773. © 2007 Wiley‐Liss, Inc.
Correlation between asparaginase sensitivity and asparagine synthetase protein content, but not mRNA, in acute lymphoblastic leukemia cell lines
Authors: Su Nan , Pan Yuan‐Xiang , Zhou Mi , Harvey Richard C. , Hunger Stephen P. , Kilberg Michael S. 
Published: May 2007

AbstractBackgroundAsparaginase (ASNase) is an essential component of most treatment protocols for childhood acute lymphoblastic leukemia (ALL). Although increased asparagine synthetase (ASNS) expression may contribute to ASNase resistance, there is conflicting data from patient samples with regard to correlation between ASNS mRNA content and ASNase sensitivity.ProcedureBoth T‐cell and B‐cell derived ALL cell lines were treated with ASNase and then monitored for cell proliferation, cell death, and ASNS mRNA and protein expression.ResultsDespite elevated ASNS mRNA following ASNase treatment, different ALL cell lines varied widely in translation to ASNS protein. Although ASNS mRNA levels did not consistently reflect ASNase sensitivity, there was an inverse correlation between ASNS protein and ASNase‐induced cell death. Expression of ASNS in an ASNase‐sensitive cell line resulted in enhanced ASNase resistance, and conversely, siRNA‐mediated inhibition of ASNS expression promoted increased drug sensitivity.ConclusionsThese observations provide an explanation for the ASNase sensitivity of ALL cells and demonstrate the importance of measuring ASNS protein rather than mRNA in predicting ASNase responsiveness. Pediatr Blood Cancer 2008;50:274–279. © 2007 Wiley‐Liss, Inc.
A novel mutation in the NF1 gene in two siblings with neurofibromatosis type 1 and bilateral optic pathway glioma
Authors: Kebudi Rejin , Tuncer Samuray , Upadhyaya Meena , Peksayar Gonul , Spurlock Gill , Yazici Hulya 
Published: May 2007

AbstractWe present the clinical and ophthalmological findings, genetic analysis, and therapy of two siblings with NF1 and bilateral OPG. In genetic analysis, a heteroduplex profile was detected in exon 4b of the NF1 gene for the affected patients and mother. Sequencing of the DNA samples identified a C > T nucleotide change in exon 4b (c484CAG > TAG). This nonsense mutation resulted in a change of glutamine to a stop codon (Q162X) and is a novel NF1 gene alteration. Pediatr Blood Cancer 2008;50:713–715. © 2007 Wiley‐Liss, Inc.