Constructive Logic with Strong Negation is a Substructural Logic. I

The goal of this two-part series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFL _ew of the substructural logic FL _ew . In this paper, it is shown that the equivalent variety semantics of N (namely, the variety of Nelson algebras) and the equivalent variety semantics of NFL _ew (namely, a certain variety of FL _ew -algebras) are term equivalent. This answers a longstanding question of Nelson [30]. Extensive use is made of the automated theorem-prover Prover9 in order to establish the result. The main result of this paper is exploited in Part II of this series [40] to show that the deductive systems N and NFL _ew are definitionally equivalent, and hence that constructive logic with strong negation is a substructural logic over FL _ew . Presented by Heinrich Wansing     

Constructive Logic with Strong Negation is a Substructural Logic. II

The goal of this two-part series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFL _ew of the substructural logic FL _ew . The main result of Part I of this series [41] shows that the equivalent variety semantics of N (namely, the variety of Nelson algebras) and the equivalent variety semantics of NFL _ew (namely, a certain variety of FL _ew -algebras) are term equivalent. In this paper, the term equivalence result of Part I [41] is lifted to the setting of deductive systems to establish the definitional equivalence of the logics N and NFL _ew . It follows from the definitional equivalence of these systems that constructive logic with strong negation is a substructural logic. Presented by Heinrich Wansing     

Pretabular varieties of modal algebras

We study modal logics in the setting of varieties of modal algebras. Any variety of modal algebras generated by a finite algebra — such, a variety is called tabular — has only finitely many subvarieties, i.e. is of finite height. The converse does not hold in general. It is shown that the converse does hold in the lattice of varieties of K4-algebras. Hence the lower part of this lattice consists of tabular varieties only. We proceed to show that there is a continuum of pretabular varieties of K4-algebras — those are the non-tabular varieties all of whose proper subvarieties are tabular — in contrast with Maksimova's result that there are only five pretabular varieties of S4-algebras.     

Proof Systems Combining Classical and Paraconsistent Negations

New propositional and first-order paraconsistent logics (called L _ω and FL _ω , respectively) are introduced as Gentzen-type sequent calculi with classical and paraconsistent negations. The embedding theorems of L _ω and FL _ω into propositional (first-order, respectively) classical logic are shown, and the completeness theorems with respect to simple semantics for L _ω and FL _ω are proved. The cut-elimination theorems for L _ω and FL _ω are shown using both syntactical ways via the embedding theorems and semantical ways via the completeness theorems. Presented by Yaroslav Shramko and Heinrich Wansing     

Equational Bases for Joins of Residuated-lattice Varieties

Given a positive universal formula in the language of residuated lattices, we construct a recursive basis of equations for a variety, such that a subdirectly irreducible residuated lattice is in the variety exactly when it satisfies the positive universal formula. We use this correspondence to prove, among other things, that the join of two finitely based varieties of commutative residuated lattices is also finitely based. This implies that the intersection of two finitely axiomatized substructural logics over FL ⁺ is also finitely axiomatized. Finally, we give examples of cases where the join of two varieties is their Cartesian product.     

Defect formation in Nd2Fe14B grains caused by Zn diffusion

Defect formation in Nd₂Fe₁₄B grains, caused by a low-pressure-pack-sublimation Zn coating process, has been investigated. The results indicate that, in the Zn-affected region, low-angle boundaries decorated with precipitates form within the Nd2Fe14B grains. Zn, which is almost insoluble in Nd₂Fe₁₄     

Kripke Incomplete Logics Containing KTB

It is shown that there is a Kripke incomplete logic in NExt(KTB ⊕ □² p → □³ p). Furthermore, it is also shown that there exists a continuum of Kripke incomplete logics in NExt(KTB ⊕ □⁵ p → □⁶ p). Presented by Michael Zakharyaschev     

A Splitting Logic in NExt(KTB)

It is shown that the normal modal logic of two reflexive points jointed with a symmetric binary relation splits the lattice of normal extensions of the logic KTB. By this fact, it is easily seen that there exists the third largest logic in the class of all normal extensions of KTB. Presented by Michael Zakharyaschev Received February 17, 2006     

Phonon densities of states of gamma-cerium and delta-cerium measured by time-of-flight inelastic neutron scattering

Time-of-flight inelastic neutron scattering spectra were measured on cerium metal at temperatures near the fcc (gamma)-to-bcc (delta) transition temperature. Phonon density-of-states (DOS) curves were extracted from data acquired over a wide range of momentum transfers. A large softening of the phonon DOS was found in going from gamma-cerium to delta-cerium, and this accounts for an increase in vibrational entropy of (0.71 +/- 0.05)k _B/atom. To be consistent with the latent heat of the gamma-delta transition, this increase in vibrational entropy must be accompanied by a large decrease in electronic entropy. The results not only confirm the recent discovery of a significant electronic contribution to the gamma-delta transition but also suggest that it may be twice that previously reported.     

On the Representation of N4-Lattices

N4-lattices provide algebraic semantics for the logic N4, the paraconsistent variant of Nelson's logic with strong negation. We obtain the representation of N4-lattices showing that the structure of an arbitrary N4-lattice is completely determined by a suitable implicative lattice with distinguished filter and ideal. We introduce also special filters on N4-lattices and prove that special filters are exactly kernels of homomorphisms. Criteria of embeddability and to be a homomorphic image are obtained for N4-lattices in terms of the above mentioned representation. Finally, subdirectly irreducible N4-lattices are described.     

The effect of hydrogen plasma on the properties of a-Si:H/a-Si1-xNx:H superlattices

Abstract

A hydrogen plasma introduced during the interrupting interval when alternating two gases affects the properties of a-Si:H/a-Si_1-xN_x:H superlattices resulting in the creation of fewer interface defects than the superlattices prepared without the hydrogen plasma.     

Extended energy-loss fine structure analysis of 3d transition metals using L ionization edges

The extended energy-loss fine structure (EXELFS) in electron-energy-loss spectroscopy has been compared experimentally with the extended X-ray absorption fine structure (EXAFS), for determining local structure around 3d transition metals. Since the EXELFS spectrum is acquired in an analytical transmission electron microscope, the probing beam can be focused to offer a lateral spatial resolution in the nanometre range, which is several orders of magnitude better than that of X-rays. Also, the microscope allows the area of interest to be imaged and analysed by other methods. However, difficulties in the analysis of EXELFS of 3d transition metals arise from the overlap of the edges in the accessible L series. EXELFS of L ionization edges of crystalline Ni and Cu were examined as test specimens. The overlapped L₁,L₂ and L₃ edges were separated and compared with the K-edge EXAFS of the same samples. The first- and second-nearest-neighbour distances from EXELFS are in agreement with those measured from EXAFS and X-ray diffraction. As a structural probe, however, the accuracy of quantitative analysis of EXAFS is still superior since the L-edge EXELFS decays more rapidly than K-edge EXAFS.     

Controllable electron-momentum filter in a δ-doped magnetically modulated semiconductor nanostructure

ABSTRACT

We have theoretically investigated the control of wave-vector filtering (WVF) by introducing δ-doping into a magnetically modulated nanostructure fabricated by depositing ferromagnetic stripes on top and bottom of a GaAs/Al_xGa_{1 ?x}As heterostructure. With the help of an improved transfer matrix method, the Schrödinger equation for electrons in this semiconductor nanostructure is solved exactly and the transmission efficient calculated numerically. We demonstrate that the WVF efficiency is associated closely with the weight and position of the δ-doping, which may be helpful for designing a controllable electron-momentum filter based on such a magnetically modulated semiconductor nanostructure.     

Electrical conductivity of Nd and Ce co-doped Gd2Zr2O7 ceramics

In this study, (Gd_{1? x} Nd _x )₂(Zr_{1? x} Ce _x )₂O₇ (0 ≤ x ≤ 0.5) ceramics have been prepared by pressureless sintering at 1973 K to investigate the influence of Nd and Ce co-doping on their electrical conductivity. The electrical conductivity of the ceramics was investigated by impedance spectroscopy measurements from 723 to 1173 K over the frequency range of 20 Hz to 2 MHz in air. The measured values obey the Arrhenius relation. For each composition, the grain conductivity gradually increases with increasing temperature from 723 to 1173 K. At a given temperature, it gradually decreases with increasing neodymium and cerium contents from x = 0 to 0.3; thereafter, the grain conductivity exhibits a slight increase with further increasing neodymium and cerium contents up to x = 0.5.     

The Adaptive Logic of Compatibility

This paper describes the adaptive logic of compatibility and its dynamic proof theory. The results derive from insights in inconsistency-adaptive logic, but are themselves very simple and philosophically unobjectionable. In the absence of a positive test, dynamic proof theories lead, in the long run, to correct results and, in the short run, sometimes to final decisions but always to sensible estimates. The paper contains a new and natural kind of semantics for S5from which it follows that a specific subset of the standard worlds-models is characteristic for S5.     

Congruence Coherent Symmetric Extended de Morgan Algebras

An algebra A is said to be congruence coherent if every subalgebra of A that contains a class of some congruence on A is a union of -classes. This property has been investigated in several varieties of lattice-based algebras. These include, for example, de Morgan algebras, p-algebras, double p-algebras, and double MS-algebras. Here we determine precisely when the property holds in the class of symmetric extended de Morgan algebras. Presented by M.E. Adams     

Extending Standard Models of ZFC to Models of Nonstandard Set Theories

We study those models of ZFCwhich are embeddable, as the class of all standard sets, in a model of internal set theory >ISTor models of some other nonstandard set theories. This revised version was published online in June 2006 with corrections to the Cover Date.     

Atomic configurations of twin boundaries and twinning dislocation in superconductor Y0.6Na0.4Ba2Cu2.7Zn0.3O7− δ

Two types of twin boundaries in superconductor Y_0.6Na_0.4Ba₂Cu_2.7Zn_0.3O_{7? δ} , the cation-centered and oxygen-centered types, and the associated twinning dislocation have been studied by high-resolution electron microscopy. The structure map projected in the [001] direction was obtained from a single image by means of the image deconvolution technique. In this map, all columns of metallic atoms appear as individual black dots, and hence the two types of twin boundaries are distinguished from each other at atomic level. It is seen that the twinning dislocation occurs when the two types of twin boundaries meet each other. The structure model of the twinning dislocation together with the two types of twin boundaries has been derived straightforwardly based on the positions of black dots seen in the deconvoluted image.     

W-algebras which are Boolean products of members of SR[1] and CW-algebras

We show that the class of all isomorphic images of Boolean Products of members of SR [1] is the class of all archimedean W-algebras. We obtain this result from the characterization of W-algebras which are isomorphic images of Boolean Products of CW-algebras.