The Cauchy Problem for a One Dimensional Nonlinear Peridynamic Model

This paper studies the Cauchy problem for a one-dimensional nonlinear peridynamic model describing the dynamic response of an infinitely long elastic bar. The issues of local well-posedness and smoothness of the solutions are discussed. The existence of a global solution is proved first in the sublinear case and then for nonlinearities of degree at most three. The conditions for finite-time blow-up of solutions are established.Comment: To appear in Journal of Differential Equations (added references, corrected typos, minor revision in Section 2, 18 pages

The Cauchy Problem for a One Dimensional Nonlinear Peridynamic Model

This paper studies the Cauchy problem for a one-dimensional nonlinear peridynamic model describing the dynamic response of an infinitely long elastic bar. The issues of local well-posedness and smoothness of the solutions are discussed. The existence of a global solution is proved first in the sublinear case and then for nonlinearities of degree at most three. The conditions for finite-time blow-up of solutions are established.Comment: To appear in Journal of Differential Equations (added references, corrected typos, minor revision in Section 2, 18 pages

Two remarks on a generalized Davey-Stewartson system

Genelleştirilmiş Davey-Stewartson (GDS) sistemi, şeklinde verilmiş bir nonlineer kısmi türevli diferansiyel denklem sistemidir. Burada kompleks değerli ve reel değerli fonksiyonlar olup, uzaysal koordinatlarının ve zamanını fonksiyonlarıdır.  Ve reel parametrelerdir. Ayrıca, katsayılar arasında şeklinde bir bağıntı sağlanmaktadır. GDS sistemi sonsuz bir genelleştirilmiş elastik ortamda yayılan quazi monokromatik dalgaların modulasyonunu karakterize eden sistem olarak önerilmiştir (Babaoğlu ve Erbay, 2004). Bu çalışmada katsayılarının işaretlerine göre Eliptik Eliptik Eliptik (EEE) ve Hiperbolik Eliptik Eliptik (HEE) durumları göz önüne alınacaktır (Eden vd., 2006). GDS sisteminin en önemli özel halleri Nonlineer Schrödinger (NLS) denklemi ve Davey-Stewartson (DS) sistemidir. NLS denkleminde olduğu gibi, DS sisteminin çözümleri de pseudo-konformal dönüşüm altında invaryant kalmaktadır. DS sisteminin Hiperbolik-Eliptik (HE) durumunda pseudo-konformal dönüşüm yardımıyla bir analitik patlama profili elde edilirken, eliptik NLS denklemi için bu invaryantlık çözümlerin patlama profillerinin anlaşılmasında temel rol oynar. Bu çalışmada GDS sisteminin de çözümlerinin pseudo-konformal dönüşüm altında invaryant kaldığı gösterilmiş ve pseudo-konformal invaryantlık kullanılarak bulunan iki yeni sonuç sunulmuştur. HEE durumda, fiziksel parametreler üzerine bazı koşullar koyarak bir patlama profili elde edilmiştir. Ancak bu koşullar bir özel “radyal” çözümün varlığı için gerekli koşullara dönüşür. EEE durumda, düzgün çözümlerin normunun zamanla cebirsel olarak sıfıra gittiği gösterilmiştir. Anahtar Kelimeler: Pseudo-konformal invaryant, Patlama profili, stabilitesi.The Generalized Davey-Stewartson (GDS) system is given by where and, are, respectively, the complex and the real valued functions of spatial coordinates and the time. The parameters and are real constants and is normalized as. The parametric relation follows from the structure of the physical constants and plays a key role in the analysis of these equations. The GDS system was derived to model dimensional wave propagation in a bulk medium composed of elastic material with couple stresses (Babaoğlu and Erbay, 2004). Four conserved quantities, corresponding to mass, momentum in the and directions and energy, were derived in (Babaoğlu et al., 2004). Furthermore, these equations were classified according to the signs of as Elliptic Elliptic Elliptic (EEE), Elliptic Elliptic Hyperbolic (EEH), Elliptic Hyperbolic Hyperbolic (EHH), Hyperbolic Elliptic Elliptic (HEE), Hyperbolic Hyperbolic Hyperbolic (HHH), Hyperbolic Elliptic Hyperbolic (HEH). Here we will only be considering EEE and HEE cases. It is well-known that many equations can be expressed as a NLS equation with additional and possibly non-local terms (Constantin, 1990). For example, in the elliptic elliptic and hyperbolic elliptic cases of the Davey-Stewartson (DS) system can be written as with, where is a linear pseudo-differential operator with a homogeneous symbol of order zero. The non-local term  acts in many ways like a cubic nonlinearity: they have similar scaling properties and the interaction between these two nonlinear terms determine the global behaviour of the solutions. In Babaoğlu et al., (2004), for the HEE and EEE cases the GDS system has been expressed as a NLS equation with additional term. This representation leads one to expect some of properties of the NLS equation to remain valid for the GDS system. In two space dimensions, the solutions of the Schrödinger equations with cubic nonlinearity (NLS) are invariant under the pseudo-conformal transformation. In addition to its inherent interests, this invariance has far reaching consequences leading to a better understanding of the blow-up profiles; global existence of the solutions; as well as their -stability. As it is the case for the NLS equation, the solutions of the DS system are invariant under the pseudo-conformal transformation. For the elliptic NLS, this invariance plays a key role in understanding the blow-up profile of solutions, whereas in the hyperbolic-elliptic case of DS system an explicit blow-up profile is obtained via the pseudo-conformal invariance. The main aim of this study, is to highlight the importance of the pseudo-conformal invariance for the GDS system (Eden et al., 2006). We start by recalling some of the work done for the classification of the GDS system as well as its conserved quantities. Then the solutions are also shown to be  invariant under a scale transformation. The corresponding conserved quantity, denoted by, is used for a derivation of the virial identity. Next, the pseudo-conformal transformation for the GDS system is stated and its invariant, denoted by, is found.  Then, we focus on the HEE case for the GDS system. Starting from a solution ansatz in the spirit of (Ozawa, 1992), a set of conditions are found on the underlying parameters. These conditions also turn out to be necessary conditions for the existence of a "radial" steady state solution. The pseudo-conformal transformation converts this steady-state solution into a time dependent one which blows-up in finite time. Finally, following an idea given in (Weinstein, 1989) we show that for, the norms of smooth solutions of the GDS system in the EEE case converge to as. Keywords: Pseudo-conformal invariance, Blow-up profile, -stability

Endothelin 1 levels in relation to clinical presentation and outcome of Henoch Schonlein purpura

<p>Abstract</p> <p>Background</p> <p>Henoch Schonlein purpura (HSP) is a common vasculitis of small vessels whereas endothelin-1 (ET-1) is usually reported elevated in vasculities and systematic inflammation. The aim of the present study was to investigate whether ET-1 levels are correlated with the clinical presentation and the outcome of HSP.</p> <p>Methods</p> <p>The study sample consisted of thirty consecutive patients with HSP. An equal number of healthy patients of similar age and the same gender were served as controls. The patients' age range was 2–12.6 years with a mean ± SD = 6.3 ± 3 years. All patients had a physical examination with a renal, and an overall clinical score. Blood and urinary biochemistry, immunology investigation, a skin biopsy and ET-1 measurements in blood and urine samples were made at presentation, 1 month later and 1 year after the appearance of HSP. The controls underwent the same investigation with the exception of skin biopsy.</p> <p>Results</p> <p>ET-1 levels in plasma and urine did not differ between patients and controls at three distinct time points. Furthermore the ET-1 were not correlated with the clinical score and renal involvement was independent from the ET-1 measurements. However, the urinary ET-1 levels were a significant predictor of the duration of the acute phase of HSP (HR = 0.98, p = 0.032, CI0.96–0.99). The ET-1 levels did not correlate with the duration of renal involvement.</p> <p>Conclusion</p> <p>Urinary ET-1 levels are a useful marker for the duration of the acute phase of HSP but not for the length of renal involvement.</p

Capturing wheat phenotypes at the genome level

Recent technological advances in next-generation sequencing (NGS) technologies have dramatically reduced the cost of DNA sequencing, allowing species with large and complex genomes to be sequenced. Although bread wheat (Triticum aestivum L.) is one of the world’s most important food crops, efficient exploitation of molecular marker-assisted breeding approaches has lagged behind that achieved in other crop species, due to its large polyploid genome. However, an international public–private effort spanning 9 years reported over 65% draft genome of bread wheat in 2014, and finally, after more than a decade culminated in the release of a gold-standard, fully annotated reference wheat-genome assembly in 2018. Shortly thereafter, in 2020, the genome of assemblies of additional 15 global wheat accessions was released. As a result, wheat has now entered into the pan-genomic era, where basic resources can be efficiently exploited. Wheat genotyping with a few hundred markers has been replaced by genotyping arrays, capable of characterizing hundreds of wheat lines, using thousands of markers, providing fast, relatively inexpensive, and reliable data for exploitation in wheat breeding. These advances have opened up new opportunities for marker-assisted selection (MAS) and genomic selection (GS) in wheat. Herein, we review the advances and perspectives in wheat genetics and genomics, with a focus on key traits, including grain yield, yield-related traits, end-use quality, and resistance to biotic and abiotic stresses. We also focus on reported candidate genes cloned and linked to traits of interest. Furthermore, we report on the improvement in the aforementioned quantitative traits, through the use of (i) clustered regularly interspaced short-palindromic repeats/CRISPR-associated protein 9 (CRISPR/Cas9)-mediated gene-editing and (ii) positional cloning methods, and of genomic selection. Finally, we examine the utilization of genomics for the next-generation wheat breeding, providing a practical example of using in silico bioinformatics tools that are based on the wheat reference-genome sequence

Instrumentos de avaliação do aleitamento materno e seu uso na prática clínica

RESUMO Objetivos Identificar instrumentos de avaliação da amamentação e sua aplicação na prática clínica, validação e adaptação transcultural. Método Revisão integrativa, realizada em seis bases de dados e em uma biblioteca eletrônica, entre agosto/2014-dezembro/2015, sem limitação temporal. Resultados Foram identificados 19 instrumentos de avaliação do AM. Destes, 12 foram validados e cinco foram adaptados transculturalmente. Quanto à aplicação, destacam-se seu uso para a avaliação do risco de desmame (BAPT) e a percepção/comportamento da mulher em amamentar (BSES-SF e IIFAS). Conclusão A identificação dos instrumentos disponíveis e de suas indicações para a avaliação do AM pode auxiliar profissionais na escolha pelo instrumento a ser utilizado, qualificando a assistência materno-infantil

Globally, songs and instrumental melodies are slower and higher and use more stable pitches than speech: A Registered Report

Both music and language are found in all known human societies, yet no studies have compared similarities and differences between song, speech, and instrumental music on a global scale. In this Registered Report, we analyzed two global datasets: (i) 300 annotated audio recordings representing matched sets of traditional songs, recited lyrics, conversational speech, and instrumental melodies from our 75 coauthors speaking 55 languages; and (ii) 418 previously published adult-directed song and speech recordings from 209 individuals speaking 16 languages. Of our six preregistered predictions, five were strongly supported: Relative to speech, songs use (i) higher pitch, (ii) slower temporal rate, and (iii) more stable pitches, while both songs and speech used similar (iv) pitch interval size and (v) timbral brightness. Exploratory analyses suggest that features vary along a “musi-linguistic” continuum when including instrumental melodies and recited lyrics. Our study provides strong empirical evidence of cross-cultural regularities in music and speech