On the Herbrand content of LK

We present a structural representation of the Herbrand content of LK-proofs with cuts of complexity prenex Sigma-2/Pi-2. The representation takes the form of a typed non-deterministic tree grammar of order 2 which generates a finite language of first-order terms that appear in the Herbrand expansions obtained through cut-elimination. In particular, for every Gentzen-style reduction between LK-proofs we study the induced grammars and classify the cases in which language equality and inclusion hold.Comment: In Proceedings CL&C 2016, arXiv:1606.0582

Extremely wideband signal shaping using one- and two-dimensional nonuniform nonlinear transmission lines

We propose a class of electrical circuits for extremely wideband (EWB) signal shaping. A one-dimensional, nonlinear, nonuniform transmission line is proposed for narrow pulse generation. A two-dimensional transmission lattice is proposed for EWB signal combining. Model equations for the circuits are derived. Theoretical and numerical solutions of the model equations are presented, showing that the circuits can be used for the desired application. The procedure by which the circuits are designed exemplifies a modern, mathematical design methodology for EWB circuits

On closure ordinals for the modal mu-calculus

The closure ordinal of a formula of modal mu-calculus mu X phi is the least ordinal kappa, if it exists, such that the denotation of the formula and the kappa-th iteration of the monotone operator induced by phi coincide across all transition systems (finite and infinite). It is known that for every alpha < omega^2 there is a formula phi of modal logic such that mu X phi has closure ordinal alpha (Czarnecki 2010). We prove that the closure ordinals arising from the alternation-free fragment of modal mu-calculus (the syntactic class capturing Sigma_2 cap Pi_2) are bounded by omega^2. In this logic satisfaction can be characterised in terms of the existence of tableaux, trees generated by systematically breaking down formulae into their constituents according to the semantics of the calculus. To obtain optimal upper bounds we utilise the connection between closure ordinals of formulae and embedded order-types of the corresponding tableaux

On closure ordinals for the modal mu-calculus

The closure ordinal of a formula of modal mu-calculus mu X phi is the least ordinal kappa, if it exists, such that the denotation of the formula and the kappa-th iteration of the monotone operator induced by phi coincide across all transition systems (finite and infinite). It is known that for every alpha < omega^2 there is a formula phi of modal logic such that mu X phi has closure ordinal alpha (Czarnecki 2010). We prove that the closure ordinals arising from the alternation-free fragment of modal mu-calculus (the syntactic class capturing Sigma_2 cap Pi_2) are bounded by omega^2. In this logic satisfaction can be characterised in terms of the existence of tableaux, trees generated by systematically breaking down formulae into their constituents according to the semantics of the calculus. To obtain optimal upper bounds we utilise the connection between closure ordinals of formulae and embedded order-types of the corresponding tableaux

Finitary proof systems for Kozen’s μ.

We present three finitary cut-free sequent calculi for the modal [my]-calculus. Two of these derive annotated sequents in the style of Stirling’s ‘tableau proof system with names’ (4236) and feature special inferences that discharge open assumptions. The third system is a variant of Kozen’s axiomatisation in which cut is replaced by a strengthening of the v-induction inference rule. Soundness and completeness for the three systems is proved by establishing a sequence of embeddings between the calculi, starting at Stirling’s tableau-proofs and ending at the original axiomatisation of the [my]-calculus due to Kozen. As a corollary we obtain a completeness proof for Kozen’s axiomatisation which avoids the usual detour through automata or games

A Cyclic Proof System for Full Computation Tree Logic

Full Computation Tree Logic, commonly denoted CTL*, is the extension of Linear Temporal Logic LTL by path quantification for reasoning about branching time. In contrast to traditional Computation Tree Logic CTL, the path quantifiers are not bound to specific linear modalities, resulting in a more expressive language. We present a sound and complete hypersequent calculus for CTL*. The proof system is cyclic in the sense that proofs are finite derivation trees with back-edges. A syntactic success condition on non-axiomatic leaves guarantees soundness. Completeness is established by relating cyclic proofs to a natural ill-founded sequent calculus for the logic

Age determination and feeding habits of Nemipterus japonicus (Bloch, 1791) in the northern Oman Sea

Age determination and feeding habits of the Japanese threadfin bream, Nemipterus japonicus, was carried out in the northern Oman Sea (Chabahar area), based on 212 specimens collected between September 2009 and May 2010. The minimum and maximum fork length and body weight were measured as 145, 258 mm and 55.31, 288.12 g. The relationship between Body Weight (BW) and Fork Length (FL) for all individuals was estimated as BW= 0.0001×FL2.83 (r2 = 0.9425, n= 212). The Vacuity Index (VI) was 55.2% that shows N. japonicus is a moderate feeder. The maximum and minimum Gastro-Somatic Index for males was in autumn and winter seasons and for females were in summer and spring. The Food Preference Indices were estimated as: crustacean (63.2%) as main food fishes (38.9%) and molluscs (36.8%) as minor food. Age determination was done by otolith sectioning. A total of 135 sagitta were sectioned. The maximum age was 5+ years old for a female with FL= 256 mm and the youngest one was 1 year old for a female with FL= 145 mm. Based on obtained results there is a significant relationship between feeding and age namely with increase of age, the feeding rate is decreased without any changes in type of feeding and food contents

Demystifying μ\mu

We develop the theory of illfounded and cyclic proof systems in the context of the modal $\mu$-calculus. A fine analysis of provability and admissibility bridges the finitary, cyclic and illfounded notions of proof for this logic and re-enforces the subtlety of two important normal form theorems: guardedness and disjunctiveness

Carbon Nanotubes-Chitosan-Molecularly Imprinted Polymer Nano-Carriers Synthesis for Nanomedicine Application

Carbon nanotube-natural biopolymer nanovectors have important potential applications in delivery system for drugs and biomolecules. In this work, the use of multi-wall CNTs as nanoreserviors for drug loading and controlled release is demonstrated .We synthesized CNT-based Drug delivery systems; MWCNT-CS nanoparticles based on an ionotropic gelation method as a sustained-release systems for the delivery of Tenofovir (hydrophilic anti-retroviral drug). Molecularly imprinted polymer used as shell for encapsulating the synthesized polymer to reduce the toxicity of CNT and improved theit application in Drug Delivery System. The prepared nanoparticles were characterized by FTIR spectroscopy. TGA was applied to study the thermal stabilities, and SEM to investi-gate the morphology. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3521