Amalgamation,interpolation and epimorphisms in algebraic logic

In his landmark paper on amalgamation published in Algebra Universalis in 1971, Don Pigozzi posed some open questions in connection with amalgamation of subclasses of cylindric algebras. Some of these questions were originally raised by Comer, Daigneault, Johnson, McKenzie and others. In this paper we give answers to all these as well as a number of other related questions. Most of the solutions were found by the authors of this paper. However, a few were contributed by others who will of course be given due credit at the appropriate points. This paper is dedicated to Don Pigozzi on his retirement. Presented by R. W. Quackenbush. The first author’s research was supported by the Hungarian National Foundation for Scientific Research grants no T30314 and T23234. The second author’s research was supported by the Hungarian National Foundation for Scientific Reserach OKTA grant no T30314. All the new results in this article were announced by Judit Madarász in the Workshop on Abstract Algebraic Logic, held in Centre de Recerca Matematica Bellaterra, Spain July 1–5, 1997. Received December 15, 2002; accepted in final form January 3, 2006.     

The novel application of Fourier thermal analysis in foundry technologies

The process of casting in sand moulds is used for a large volume of castings manufactured in the world. Internal channels and complex geometries of these products are formed by the placement of cores within the mould cavity. Resin-bound sand mixtures are essential ingredients in engine component manufacturing. In this study, a state-of-the-art application of Fourier thermal analysis in foundry technologies is presented. Investigation of decomposition phenomena of resin-bound moulding materials during casting production is a brand new area to use the potential of thermal sciences. Temperature measurements in test samples of standard types of moulding mixtures were performed. The registered cooling curves were processed by a numerical iteration algorithm to determine the amount of heat absorbed during degradation of the moulding material. Thermogravimetric analysis (TG) and differential thermal analysis (DTA) of sand mixtures were carried out to compare the results of the Fourier thermal analysis with TG and DTA curves.     

Isolation and structure determination of new 4,12-dideoxyphorbol esters from Euphorbia pannonica Host.

Phytochemical study of the aerial parts of Euphorbia pannonica led to the isolation of two new tigliane diterpenes, 4,12-dideoxy(4β)phorbol-20-benzoate-13-isobutyrate (1) and 4,12-dideoxy(4β)phorbol-20-benzoate-13-isovalerianate (2). The structures and relative stereochemistry were elucidated on the basis of extensive spectroscopic analyses, including 1D and 2D NMR experiments (¹H NMR, JMOD, COSY, NOESY, HSQC and HMBC).     

Low-temperature combustion chemistry of biofuels: pathways in the initial low-temperature (550 K-750 K) oxidation chemistry of isopentanol

The branched C(5) alcohol isopentanol (3-methylbutan-1-ol) has shown promise as a potential biofuel both because of new advanced biochemical routes for its production and because of its combustion characteristics, in particular as a fuel for homogeneous-charge compression ignition (HCCI) or related strategies. In the present work, the fundamental autoignition chemistry of isopentanol is investigated by using the technique of pulsed-photolytic Cl-initiated oxidation and by analyzing the reacting mixture by time-resolved tunable synchrotron photoionization mass spectrometry in low-pressure (8 Torr) experiments in the 550-750 K temperature range. The mass-spectrometric experiments reveal a rich chemistry for the initial steps of isopentanol oxidation and give new insight into the low-temperature oxidation mechanism of medium-chain alcohols. Formation of isopentanal (3-methylbutanal) and unsaturated alcohols (including enols) associated with HO(2) production was observed. Cyclic ether channels are not observed, although such channels dominate OH formation in alkane oxidation. Rather, products are observed that correspond to formation of OH viaβ-C-C bond fission pathways of QOOH species derived from β- and γ-hydroxyisopentylperoxy (RO(2)) radicals. In these pathways, internal hydrogen abstraction in the RO(2)? QOOH isomerization reaction takes place from either the -OH group or the C-H bond in α-position to the -OH group. These pathways should be broadly characteristic for longer-chain alcohol oxidation. Isomer-resolved branching ratios are deduced, showing evolution of the main products from 550 to 750 K, which can be qualitatively explained by the dominance of RO(2) chemistry at lower temperature and hydroxyisopentyl decomposition at higher temperature.     

Comparative study of the in vitro bioactivities of Bupleurum rigidum and B. fruticescens

Decoctions of the aerial parts of either Bupleurum rigidum or B. fruticescens are equally used in certain parts of Spain for the treatment of topical and musculoskeletal inflammations. In the present paper, their phytochemical profile and pharmacological value has been compared. After chromatographic and spectral analyses we could establish the presence of rutin and absence of chlorogenic acid in B. fruticescens, whilst the contrary applies to B. rigidum, providing a means to chemically differentiate extracts and dry materials from the two species. Their free radical scavenging and antiperoxidative activities were similar, with B. fruticescens being more active overall. The infusions of both Bupleurum species also showed similar anti-inflammatory activity when tested by NF-kappaB assay (40% and 42% at 60 microg x mL(-1)), as well as in a hexosaminidase exocytosis assay (30% at 50 microg x mL(-1)). Antimigratory effects on rat melanoma B16F10 showed significant activity for both infusions, with B. rigidum twice as potent as B. fruticescens, the activity of the latter not being fully explained by its content of rutin. Taking all these results together, we can conclude that, in the selected experimental models, there exist an in vitro bioequivalence of the infusions from both species, which is in agreement with the majority of ethnopharmacological reports.     

M?ssbauer study of peroxynitrito complex formation with FeIII-chelates

The reaction of the μ-oxo-diiron(III)-L complex (L = EDTA, ethylene diamine tetraacetate, HEDTA, hydroxyethyl ethylene diamine triacetate, and CyDTA, cyclohexane diamine tetraacetate) with peroxynitrite in alkaline solution was studied by M?ssbauer spectroscopy using rapid-freezing technique. These complexes yield an (L)Fe^III(η ²-O $_{2})^{3-}$ complex ion when they react with hydrogen peroxide and the formation of the peroxide adduct results in a deep purple coloration of the solution. The same color appears when the reaction occurs with peroxinitrite. Although spectrophotometry indicated some difference between the molar extinction coefficients of the peroxo and the peroxinitrito adducts, the M?ssbauer parameters proved to be the same within experimental error. It is concluded that the peroxynitrite ion decomposes when reacting with Fe^III(L) and the peroxo adduct forms.     

Cationation of dimethylallyl alcohols by B(C6F5)3 as models of the (Re)initiation reaction in the bio‐inspired cationic polymerization of isoprene

The polymerization of isoprene initiated by dimethylallyl alcohols (DMAOH) in the presence of Lewis acids (LAs) as coinitiators has been selected as a potential model of the proposed cationic mechanisms involved in natural rubber (NR) biosynthesis. In view to investigate the activation/ionization mechanism of the allyl alcohol chain terminus (PIAllOH), which was shown to exist in NR, different isomers of DMAOH were used as simple models of polyisoprene chain‐end structures in the presence of tris(pentafluorophenyl)borane (BLA) as a LA. It is shown that cationation of 3,3‐DMAOH by BLA proceeds by direct OH abstraction. However, this process is strongly retarded in the presence of 2,6‐di‐tert‐butylpyridine (d^tBP), due to the formation of different BLA complexes, one with 3,3‐DMAOH, active for cationation, and a dormant one involving its ionized form 3,3‐DMAO^?. The monomer generated in situ by ionization/proton elimination steps subsequently adds on the primary allylic carbocation form, then resulting in the formation of oligoisoprenes, whereas the tertiary carbocation form of the allylic carbocation yields exclusively to proton elimination and isoprene formation, a possible mechanism of chain‐end termination. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011.     

Approximate convexity of Takagi type functions

Given a bounded function Φ:R→R, we define the Takagi type function TΦ:R→R by

     

Strengthening of strong and approximate convexity?

Let X be a real linear space and $D\subseteq X$ be a nonempty convex subset. Given an error function E:[0,1]×(D?D)?????{+??} and an element $t\in\left]0,1\right[$ , a function f:D??? is called (E,t)-convex if $$f(tx+(1-t)y)\le tf(x)+(1-t)f(y)+E(t,x-y)$$ for all x,y??D. The main result of this paper states that, for all a,b??(???{0})+{0,t,1?t} such that {a,b,a+b}??????, every (E,t)-convex function is also $\big(F,\frac{a}{a+b}\big)$ -convex, where $$F(s,u):=\frac{{(a+b)}^2s(1-s)}{t(1-t)}E\left(t,\frac{u}{a+b}\right),\qquad (u\in (D-D), \, s\in\left]0,1\right[).$$ As a consequence, under further assumptions on E, the strong and approximate convexity properties of (E,t)-convex functions can be strengthened.