11 research outputs found

    On limits of sequences of algebraic elements over a complete field

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    Let K be a complete field with respect to a real non-trivial valuation v, and ν̅be the extension of v to an algebraic closure K̅ of K. A well-known result of Ostrowski asserts that the limit of a Cauchy sequence of elements of K̅ does not always belong to K̅ unless K̅is a finite extension of K. In this paper, it is shown that when a Cauchy sequence { bn} of elements of K̅ is such that the sequence { [K(bn): K] } of degrees of the extensions K(bn)/K does not tend to infinity as n approaches infinity, then {bn}has a limit in K̅.We also give a characterization of those Cauchy sequences {bn} of elements of K̅whose limit is not in K̅,which generalizes a result of Alexandru, Popescu and Zaharescu

    On pth roots in Henselian valued fields

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    Let v be a Henselian valuation of arbitrary rank of a field K of characteristic zero with value group G and residue field of characteristic p > 0. Suppose that K contains a primitive pth root of unity. It is well known that if d is an element of K with ν(d)>pν(p)/p-1 then (1 + d)1/P ε K.In this article we investigate whether is the smallest among all elements λ of G which have the property that whenever v(d)> λ,d ε K then 1 + d is a pth power in K

    A Characterization of Krasner's Constant

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    Let v be a henselian valuation of any rank of a eld K with value group G and v be its unique prolongation to a xed algebraic closure K of K: For an element of K\K; which is separable over K; let !K () denote the well known Krasner's constant given by maxfv( 6= runs over K conjugates of g: In 1946, Krasner proved that if belonging to K is such that v( ) > !K (); then K() K( ): In this paper, we investigate whether !K () is the smallest among all the elements of the divisible closure of G which have the property that whenever v( ) > ; 2 K; then K() K( )

    Difference polynomials and their generalizations

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    A well-known result of Ehrenfeucht states that a difference polynomial f(X)-g(Y) in two variables X, Y with complex coefficients is irreducible if the degrees of f and g are coprime. Panaitopol and Stefãnescu generalized this result, by giving an irreducibility condition for a larger class of polynomials called “generalized difference polynomials”. This paper gives an irreducibility criterion for more general polynomials, of which the criterion of Panaitopol and Stefãnescu is a special case

    Difference Polynomials and Their Generalizations

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    this paper, we study irreducibility conditions of more general polynomials given by F (X; Y ) = cX ; c 2 k ; e 1; such that there exists t; 1 t e satisfying deg Y F (X; Y ) = degP t (Y ) = d and degP i (Y ) < di=t for i 6= t; 1 i e: Such a polynomial F (X; Y ) will be referred to as a quasi-dierence polynomial of the type (d; t) with respect to X: In 1990, L. Panaitopol and D. Stefanescu proved that a quasi-dierence polynomial of the type (d; t) with d and t coprime is irreducible over k[X] (cf. [5, Theorem 6]). In this direction, we go further and give an irreducibility criterion for a quasi-dierence polynomial of the type (d; t) with d and t not necessarily coprime, of which the criterion of Panaitopol and Stefanescu is a special case. Our method of proof is dierent from the one employed in [2] and [5], and is based on the idea of the proof of the Generalized Eisenstein's Irreducibility Criterion given in [4

    Assessment of smear layer removing efficacy of different irrigation activation devices in mandibular premolar teeth using a scanning electron microscope: An in vitro comparative study

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    Aim: The purpose of this study was to assess and compare the effectiveness of three different irrigation activation systems in removing smear layer in single-rooted mandibular premolars using scanning electron microscope (SEM). Materials and Methods: Fifty-six extracted single-rooted mandibular premolars were included in the study (n = 56). The teeth were decoronated, working length was determined, and canals were prepared till #30/0.09, with 5.25% sodium hypochlorite and saline as working solution. Final irrigation was performed with 5 mL of 17% ethylenediaminetetraacetic acid solution using three different activation systems. Teeth were randomly divided into four groups: Group A (control group) – conventional syringe irrigation with 30-G single side-vented needle; Group B (passive ultrasonic irrigation [PUI] method) – PUI with #20 Irrisafe ultrasonic files activated for 1 min; Group C (sonic activation) – EndoActivator system using the yellow tip (#20/0.04) activated for 1 min; and Group D – Tornado Disinfection Kit using GF Brush for 20–30 s as per the manufacturer's instructions. The samples were sectioned and subjected to SEM at × 2500 magnification. The efficacy of smear layer removal was assessed and scored by two operators. The collected data were analyzed statistically using Chi-square test (P < 0.05). Results: There was no statistically significant difference observed between the three different activation groups and the control group (P < 0.05). Conclusion: PUI performed better than all the study groups in removing smear layer from coronal, middle, and apical third of root canals. EndoActivator and Tornado Disinfection Kit performed similar in coronal and middle third, but the efficacy in apical third was inferior to the PUI group

    Extraction and characterization of ultrasound assisted extraction: improved functional quality of pectin from jackfruit (Artocarpus heterophyllus Lam.) peel waste

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    Jackfruit peels are potential waste for valorization and extraction of pectin and quality of pectin is a function of extraction conditions. Present study evaluates the effect of low temperature (LT) extraction; mediated through ultrasonication on the quality of pectin from jackfruit peel waste (JP). We first optimized ultrasound assisted extraction (UAE) process through response surface methodology (RSM) based on a Box-Behnken design (BBD) and arrived at optimal extraction conditions with maximum pectin yield and galacturonic acid content (GalA). Pectin extracted at LT and conventional high temperature (HT) referred as UAE-P and CE-P respectively were compared for their technological and structural properties. GalA content ranged between 65.53 and 68.65% in CE-P and UAE-P respectively. UAE-P had methoxyl content (5.58), protein (1.69%), molecular weight (149.67), total phenolic content (1645 mg GAE/100 g), and antioxidant capacity (123.76 µmol TE/g). There were significant (p < 0.05) differences in the Arabinose (Ara) content, FTIR spectra and functionality of pectin extracted at LT and HT. The Ara content was ~ twofold higher while antioxidant activity was ~ 1.66-fold higher in LT extracted UAE-P pectin. Hypoglycemic activity as determined by in vitro α–amylase and α–glucosidase inhibitory activity was significantly higher (p < 0.05) in UAE-P in comparison to CE-P. The DE value of UAE-P (38.11%) was low (< 50%) thus it was categorized as low methoxyl pectin. Results suggests that the UAE is potential efficient green method to obtain high quality food grade pectin with higher yield and functionality in short duration

    A 12-year-old Child with Trichinellosis, Pyomyositis and Secondary Osteomyelitis

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    Trichinellosis is a parasitic infestation affecting the skeletal muscles. Cases of trichinellosis in humans have been reported from most regions of the world. However, a review of literature revealed only two reported cases of human trichinellosis in India. Further, a diagnosis of superimposed pyomyositis in trichinellosis with secondary osteomyelitis has not been reported to our knowledge. This article reports this rare case presentation in a 12-year-old child. Timely intervention helped prevent long-term morbidity in our patient. In our case report, we also discuss in detail the pathogenesis of such a condition and discuss the role of imaging modalities and an early magnetic resonance imaging (MRI) to diagnose the condition and start an early treatment
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