scholarly journals Novel Approach of Existence of Solutions to the Exponential Equation (3m2 + 3) x + (7m2 +1) y = z2

Author(s):  
R.Vanajaq, Et. al.

In this manuscript the exponential equation (3m2 + 3) x + (7m2 +1) y = z2 where m Î Z in three variables for the occurrence of solutions belonging to the set  of all integers or the concerned equation has no solution for various alternatives of m is investigated.

2020 ◽  
Vol 169 (1) ◽  
pp. 593-611 ◽  
Author(s):  
Tomasz Dębiec ◽  
Markus Schmidtchen

Abstract We present a two-species model with applications in tumour modelling. The main novelty is the coupling of both species through the so-called Brinkman law which is typically used in the context of visco-elastic media, where the velocity field is linked to the total population pressure via an elliptic equation. The same model for only one species has been studied by Perthame and Vauchelet in the past. The first part of this paper is dedicated to establishing existence of solutions to the problem, while the second part deals with the incompressible limit as the stiffness of the pressure law tends to infinity. Here we present a novel approach in one spatial dimension that differs from the kinetic reformulation used in the aforementioned study and, instead, relies on uniform BV-estimates.


2019 ◽  
Vol 476 (24) ◽  
pp. 3705-3719 ◽  
Author(s):  
Avani Vyas ◽  
Umamaheswar Duvvuri ◽  
Kirill Kiselyov

Platinum-containing drugs such as cisplatin and carboplatin are routinely used for the treatment of many solid tumors including squamous cell carcinoma of the head and neck (SCCHN). However, SCCHN resistance to platinum compounds is well documented. The resistance to platinum has been linked to the activity of divalent transporter ATP7B, which pumps platinum from the cytoplasm into lysosomes, decreasing its concentration in the cytoplasm. Several cancer models show increased expression of ATP7B; however, the reason for such an increase is not known. Here we show a strong positive correlation between mRNA levels of TMEM16A and ATP7B in human SCCHN tumors. TMEM16A overexpression and depletion in SCCHN cell lines caused parallel changes in the ATP7B mRNA levels. The ATP7B increase in TMEM16A-overexpressing cells was reversed by suppression of NADPH oxidase 2 (NOX2), by the antioxidant N-Acetyl-Cysteine (NAC) and by copper chelation using cuprizone and bathocuproine sulphonate (BCS). Pretreatment with either chelator significantly increased cisplatin's sensitivity, particularly in the context of TMEM16A overexpression. We propose that increased oxidative stress in TMEM16A-overexpressing cells liberates the chelated copper in the cytoplasm, leading to the transcriptional activation of ATP7B expression. This, in turn, decreases the efficacy of platinum compounds by promoting their vesicular sequestration. We think that such a new explanation of the mechanism of SCCHN tumors’ platinum resistance identifies novel approach to treating these tumors.


2020 ◽  
Vol 51 (3) ◽  
pp. 544-560 ◽  
Author(s):  
Kimberly A. Murphy ◽  
Emily A. Diehm

Purpose Morphological interventions promote gains in morphological knowledge and in other oral and written language skills (e.g., phonological awareness, vocabulary, reading, and spelling), yet we have a limited understanding of critical intervention features. In this clinical focus article, we describe a relatively novel approach to teaching morphology that considers its role as the key organizing principle of English orthography. We also present a clinical example of such an intervention delivered during a summer camp at a university speech and hearing clinic. Method Graduate speech-language pathology students provided a 6-week morphology-focused orthographic intervention to children in first through fourth grade ( n = 10) who demonstrated word-level reading and spelling difficulties. The intervention focused children's attention on morphological families, teaching how morphology is interrelated with phonology and etymology in English orthography. Results Comparing pre- and posttest scores, children demonstrated improvement in reading and/or spelling abilities, with the largest gains observed in spelling affixes within polymorphemic words. Children and their caregivers reacted positively to the intervention. Therefore, data from the camp offer preliminary support for teaching morphology within the context of written words, and the intervention appears to be a feasible approach for simultaneously increasing morphological knowledge, reading, and spelling. Conclusion Children with word-level reading and spelling difficulties may benefit from a morphology-focused orthographic intervention, such as the one described here. Research on the approach is warranted, and clinicians are encouraged to explore its possible effectiveness in their practice. Supplemental Material https://doi.org/10.23641/asha.12290687


2015 ◽  
Vol 21 ◽  
pp. 128
Author(s):  
Kaniksha Desai ◽  
Halis Akturk ◽  
Ana Maria Chindris ◽  
Shon Meek ◽  
Robert Smallridge ◽  
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2020 ◽  
Vol 7 (4) ◽  
pp. 246-261
Author(s):  
Anthony Isacco ◽  
Paul B. Ingram ◽  
Katie Finn ◽  
John D. Dimoff ◽  
Brendan Gebler

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