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  • Author or Editor: Tarek Ahmed x
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We prove that every (not necessarily locally finite) polyadic Heyting algebra of infinite dimension is representable in some concrete sense. We also show that this class has the super amalgamation property. As a byproduct we infer that a certain infinitary extension of predicate intuitionistic logic, or equivalently, the intuitionistic fragment of Keisler’s infinitary logics, is complete and enjoys the Craig interpolation property.

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Let (Kα: αω) be a system of varieties definable by schemas. We characterize the amalgamation base, strong amalgamation base, and super amalgamation base of the class \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $S\mathfrak{N}\mathfrak{r}_\alpha $ \end{document}Kα+ω at this abstract level.

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Let α be an infinite ordinal. Let RCAα denote the variety of representable cylindric algebras of dimension α. Modifying Andréka’s methods of splitting, we show that the variety RQEAα of representable quasi-polyadic equality algebras of dimension α is not axiomatized by a set of universal formulas containing only finitely many variables over the variety RQAα of representable quasi-polyadic algebras of dimension α. This strengthens a seminal result due to Sain and Thompson, answers a question posed by Andréka, and lifts to the transfinite a result of hers proved for finite dimensions > 2. Using the modified method of splitting, we show that all known complexity results on universal axiomatizations of RCAα (proved by Andréka) transfer to universal axiomatizations of RQEAα. From such results it can be inferred that any algebraizable extension of L ω,ω is severely incomplete if we insist on Tarskian square semantics. Ways of circumventing the strong non-negative axiomatizability results hitherto obtained in the first part of the paper, such as guarding semantics, and /or expanding the signature of RQEAω by substitutions indexed by transformations coming from a finitely presented subsemigroup of (ω ω, ○) containing all transpositions and replacements, are surveyed, discussed, and elaborated upon.

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We construct an infinite dimensional quasi-polyadic equality algebra \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\mathfrak{A}$ \end{document} such that its cylindric reduct is representable, while \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\mathfrak{A}$ \end{document} itself is not representable.

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Abstract

For β an ordinal, let PEAβ (SetPEAβ) denote the class of polyadic equality (set) algebras of dimension β. We show that for any infinite ordinal α, if APEAα is atomic, then for any n < ω, the n-neat reduct of A, in symbols rnAB, is a completely representable PEAn (regardless of the representability of A). That is to say, for all non-zero arnA, there is a BaSetPEAn and a homomorphism fa:rnAB such that fa(a) ≠ 0 and fa(X)=xXfa(x) for any X=A for which X exists. We give new proofs that various classes consisting solely of completely representable algebras of relations are not elementary; we further show that the class of completely representable relation algebras is not closed under ≡∞,ω. Various notions of representability (such as ‘satisfying the Lyndon conditions’, weak and strong) are lifted from the level of atom structures to that of atomic algebras and are further characterized via special neat embeddings. As a sample, we show that the class of atomic CAns satisfying the Lyndon conditions coincides with the class of atomic algebras in ElS c Nr n CA ω, where El denotes ‘elementary closure’ and S c is the operation of forming complete subalgebras.

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Abstract

Background

Otitis media with effusion is the most common cause of conductive hearing loss in the pediatric population. Insertion of ventilation tubes with or without adenoidectomy is the accepted and standard surgical procedure. CO2 laser myringotomy without tube placement has been advocated as an alternative treatment.

Aim

To compare long-term follow-up results of laser versus classical myringotomy with ventilation tube insertion over five years.

Materials and Methods

86 patients with bilateral otitis media with effusion were divided into two groups: laser myringotomy group and myringotomy with ventilation tube insertion group, with follow-up in hearing results and recurrence rates over five years.

Results

The mean patency time of myringotomy in laser group was 23 days, while the mean patency time of the ventilation tubes ears was 4.0 months in myringotomy group. Twelve patients in laser group (13.9%) showed a recurrent otitis media with effusion compared to 9 patients in myringotomy group (10.4%).

Conclusion

Laser fenestration is a less effective alternative to myringotomy and tube placement. The recurrence rates after both procedures did not show statistical significance over long follow-up. It might be considered as an effective alternative to classical surgery and ideal for short-term ventilation.

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Abstract

Fix 2 < n < ω and let CAn denote the class of cyindric algebras of dimension n. Roughly CAn is the algebraic counterpart of the proof theory of first order logic restricted to the first n variables which we denote by Ln. The variety RCAn of representable CAns reflects algebraically the semantics of L n. Members of RCAn are concrete algebras consisting of genuine n-ary relations, with set theoretic operations induced by the nature of relations, such as projections referred to as cylindrifications. Although CAn has a finite equational axiomatization, RCAn is not finitely axiomatizable, and it generally exhibits wild, often unpredictable and unruly behavior. This makes the theory of CAn substantially richer than that of Boolean algebras, just as much as Lω,ω is richer than propositional logic. We show using a so-called blow up and blur construction that several varieties (in fact infinitely many) containing and including the variety RCAn are not atom-canonical. A variety V of Boolean algebras with operators is atom canonical, if whenever 𝔄 V is atomic, then its Dedekind-MacNeille completion, sometimes referred to as its minimal completion, is also in V. From our hitherto obtained algebraic results we show, employing the powerful machinery of algebraic logic, that the celebrated Henkin-Orey omitting types theorem, which is one of the classical first (historically) cornerstones of model theory of L ω,ω, fails dramatically for L n even if we allow certain generalized models that are only locallly clasfsical. It is also shown that any class K such that NrnCAωCRCAn¯K¯ScNrnCAn+3 , where CRCAn is the class of completely representable CAns, and Sc denotes the operation of forming dense (complete) subalgebras, is not elementary. Finally, we show that any class K such that SdRaCAω¯K¯ScRaCA5 is not elementary, where Sd denotes the operation of forming dense subalgebra.

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Abstract

Although glimepiride (GLM) is the first-line treatment of Type II diabetes, low extraction recovery is still a significant limitation in previous plasma analysis methods. An optimized solid-phase extraction method of GLM in human plasma with excellent extraction recovery, 100 ± 0.06%, was achieved using liquid chromatography-electrospray ionization tandem mass spectrometry and Gliclazide (GLZ) as an internal standard. GLM was extracted from 100 µL plasma sample using Sep-Pak® vac 1cc (100 mg) C18 column and methylene chloride: methanol (2: 1, v/v) as eluant. Both GLM and GLZ were monitored by a triple quad mass spectrometer applying positive multiple reaction monitoring mode (+MRM). The protonated precursor ions and product ions of GLM and GLZ were m/z 491(352), and m/z 324 (127), respectively. The detection and measurement of low levels of GLM in human plasma reached to picogram range (limit of detection (LOD) = 60 pg/mL, limit of quantification (LOQ) = 200 pg/mL). The method was validated in terms of selectivity, linearity, recovery, accuracy, and precision. The method was successfully applied to the pharmacokinetic study of GLM following oral administration of 1 mg GLM tablets to 12 healthy volunteers.

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Abstract

We prove completeness, interpolation, decidability and an omitting types theorem for certain multi-dimensional modal logics where the states are not abstract entities but have an inner structure. The states will be sequences. Our approach is algebraic addressing varieties generated by complex algebras of Kripke semantics for such logics. The algebras dealt with are common cylindrification free reducts of cylindric and polyadic algebras. For finite dimensions, we show that such varieties are finitely axiomatizable, have the super amalgamation property, and that the subclasses consisting of only completely representable algebras are elementary, and are also finitely axiomatizable in first order logic. Also their modal logics have an N P complete satisfiability problem. Analogous results are obtained for infinite dimensions by replacing finite axiomatizability by finite schema axiomatizability.

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In this work, a novel, simple, and quick capillary zone electrophoresis (CZE) method was proposed for simultaneous analysis of benazepril (BEN) with other co-administrated antihypertensive drugs, amlodipine besylate (AML) and hydrochlorothiazide (HCT), using a diode array detector (DAD). A fused silica capillary (78.5 cm total length, 70 cm effective length, and 75 μm id) was used in separation using a 40 mM phosphate buffer pH 7.5 as a running background electrolyte (BGE) under a positive potential of 30 KV, at a stable temperature of 25 °C for capillary during separation. Hydrodynamic injections were performed for 12 s at 50 mbar, and detection was performed at 210 nm for AML and BEN, at 225 nm for HCT, and at 232 nm for xipamide (XIP) added as an internal standard (IS). Separation of the three analyzed drugs and the IS was performed in less than 8 min. Migration times were 4.06, 5.23, 6.69, and 7.3 min for AML, HCT, BEN, and XIP, respectively. The findings proved that the proposed method was linear in the range of 10–80 μg/mL for all drugs with correlation coefficients >0.9994. The limit of detection (LOD) values of AML, HCT, and BEN were 1.004, 1.224, and 0.896 μg/mL, respectively, whereas the limit of quantification (LOQ) values were 3.124, 3.727, and 2.749 μg/mL for the cited drugs, respectively. Peak identity and purity were confirmed by DAD. The developed CZE method was applied for the analysis of the three antihypertensive drugs successfully in their combined pharmaceutical tablets, and it can be used for the quality control of single-pill combination (SPC) samples of these drugs in short time.

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