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Let q be a quadratic form over a field K of characteristic different from 2. We investigate the properties of the smallest positive integer n such that -1 is a sum of n values represented by q in several situations. We relate this invariant (which is called the q-level of K) to other invariants of K such as the level, the u-invariant and the Pythagoras number of K. The problem of determining the numbers which can be realized as a q-level for particular q or K is studied. We also observe that the q-level naturally emerges when one tries to obtain a lower bound for the index of the subgroup of non-zero values represented by a Pfister form q. We highlight necessary and/or sufficient conditions... 

During the last decade, reports show that the incidence and prevalence of Alzheimer's disease (AD) and other dementias have significantly increased. AD poses an enormous escalating threat to health services and resources. Early diagnosis of AD is recognized as one of the major challenges and primary aims in scientific communities. With the arrival of nanoscience and nanotechnology to medicine, hopes for early diagnosis and treatment of AD have considerably increased. To this end, nanobioresearchers are focused on three major areas consisting of early detection and recognition, biological markers and diagnosis, and pharmacotherapy. Several efforts are in progress for the discovery of new... 

In shell and tube heat exchangers, deep cracks can occur in tube-to-tubesheet welding and repairing such cracks is an impossible task which makes these tubes totally out of service. To preserve the thermal and mechanical integrity of heat exchanger, a series of rods is passed through these tubes and then are welded to tubesheets from both ends. Due to the increased damages in the vicinity of plugged tubes, the effect of plugging the tubes in the surrounding tubes and tubesheet failure is investigated. To this end, using CFD analysis, the temperature and pressure were calculated throughout the heat exchanger and then, the deformations and stresses of the tubes and tubesheets were computed... 

In a shell and tube heat exchanger, the failure of tube-to-tubesheet welds results in high-pressure water jet which erodes the refractory in front of the tubesheet. Finite element method was employed to simulate the welding process and post weld heat treatment (PWHT) to find the factors affecting the failure in tube-to-tubesheet weldments. Residual stresses in two different geometries of tube-to-tubesheet weldment were calculated through uncoupled thermal-structural analysis. The results showed that the values of residual stresses are higher in heat exchanger of site 1 than site 2 due to more weld passes and geometry of connection. Also, the maximum stress in site 1 occurs at the shellside... 

In a shell and tube heat exchanger, the failure of tube-to-tubesheet welds results in high-pressure water jet which erodes the refractory in front of the tubesheet. Finite element method was employed to simulate the welding process and post weld heat treatment (PWHT) to find the factors affecting the failure in tube-to-tubesheet weldments. Residual stresses in two different geometries of tube-to-tubesheet weldment were calculated through uncoupled thermal-structural analysis. The results showed that the values of residual stresses are higher in heat exchanger of site 1 than site 2 due to more weld passes and geometry of connection. Also, the maximum stress in site 1 occurs at the shellside... 

The effect of the autofrettage process on high pressure cylinders has been investigated. Both numerical and experimental techniques have been used for the investigation. It was observed that the best autofrettage pressure for raising the pressure capacity of the cylinder was the pressure Py2 which is just sufficient to bring the outer surface of the cylinder to yielding. Pressures higher than Py2 will have the inverse effect. It was found that the number of autofrettage stages has no effect on pressure capacity. It was also shown that to reduce the flow stress within the wall of the cylinder, the autofrettage pressure must be greater than the working pressure. For pressures lower than... 

This is a variation on a theme of Bayer-Fluckiger, Shapiro, and Tignol related to hyperbolic involutions. More precisely, criteria for the hyperbolicity of involutions of quadratic extensions of simple algebras and involutions of the form σ ⊗ τ and σ ⊗ ρ, where σ is an involution of a central simple algebra A, τ is the nontrivial automorphism of a quadratic extension of the center of A, and ρ is an involution of a quaternion algebra are obtained  

The aim of this article is to provide a characterization of quadratic forms of low dimension such that the canonical involutions of their Clifford algebras are hyperbolic  

Involutions of the Clifford algebra of a quadratic space induced by orthogonal symmetries are investigated  

For every rotation (Formula presented.) of the Euclidean space (Formula presented.) ((Formula presented.)), we find an upper bound for the number (Formula presented.) such that (Formula presented.) is a product of (Formula presented.) rotations by an angle (Formula presented.) ((Formula presented.)). We also find an upper bound for the number (Formula presented.) such that (Formula presented.) can be written as a product of (Formula presented.) full rotations by an angle (Formula presented.). © 2017 Australian Mathematical Publishing Association Inc  

This article aims to present a geometric interpretation of the simplicity of the rotation group of three-dimensional Euclidean space. Some historical remarks on the subject and an overview of a collection of different proofs of this result are also given  

Shot peening is one of the most effective surface treatments for improving the fatigue strength of machine elements. In this paper, a new finite element-based model to predict the effect of coverage on the surface state is proposed and critically discussed. By this model, the effects of Rayleigh damping, mesh size, and target dimensions on residual stress profile are investigated using a random impingement simulation of shot peening. Moreover, the model enables the realistic simulation of shot peening process with an affordable computational time with respect of present approaches without reducing the number of impacts and analysis accuracy: the computational time was reduced by 25% in... 

Once in biological fluids, the surface of nanoparticles (NPs) is rapidly covered with a layer of biomolecules (i.e., the "protein corona") whose composition strongly determines their biological identity, regulates interactions with biological entities including cells and the immune system, and consequently directs the biological fate and pharmacokinetics of nanoparticles. We recently introduced the concept of a "personalized protein corona" which refers to the formation of different biological identities of the exact same type of NP after being exposed to extract plasmas from individuals who have various types of diseases. As different diseases have distinct metabolomic profiles and... 

The subject of this study is to investigate the effect of repair on the fatigue life of tubular joints. Six cracked specimens previously subjected to fatigue loading underwent weld repair. Two of these specimens were shot peened before primary fatigue loading. It is shown that repair for the original specimens increases the fatigue life by roughly 150%. The increase of fatigue life for shot peened and repaired specimens is around 105%. The in-depth residual stresses are measured on the repaired joints before and after fatigue loading. It can be stated that repair made a remarkable improvement on the fatigue behavior of tubular joints examined in this investigation. However, where repair is... 

Extensive wind tunnel tests have been conducted to investigate the unsteady flow field over and behind a 2D model of a 660 kW wind turbine blade section in pitching motion. The surface pressure and wake dynamic pressure variation at a distance of 1.5 chord length from trailing edge were measured by pressure transducers during several oscillating cycles at 3 reduced frequencies and oscillating amplitudes. Moreover, form drag and linear momentum deficit are extracted and compared at various conditions. The results show that the wake velocity field and surface pressure of the model have similar behavior before and after the airfoil beyond the static stall angle of attack. In addition, the... 

A ternary dielectric is made of high density polyethylene (HDPE) and organoclay (OC) nanocomposites, through mixing granuls of ethylene vinyl acetate (EVA). The morphological properties of nanocomposites are examined using X-ray diffraction (XRD) spectra and transmission electron microscopy (TEM) which intercalate/exfoliate morphology of clay particles. It is shown that the electrical and mechanical properties of HDPE/EVA binary blend will be enhanced significantly when OC was treated with EVA compound. The insulation material which is developed in this work can be employed to insulate the adjacent core steel sheets of a high voltage transformer  

Shot peening is the most common surface treatment employed to enhance the fatigue performance of structural metallic materials and often carried out after other surface treatments. This paper mainly focuses on the effects of initial conditions of surface such as initial stress filed and hardness profile on shot peening residual stress field. The residual stress distribution induced by shot peening is obtained using Hertzian contact theory and elastic–plastic evaluation after yielding occurred during impingement and rebound of shots. Elastic plastic calculations are performed using different hardening models considering Bauschinger effect. The present model is able to predict redistribution... 

An offshore structure is exposed to environmental loading and cyclic stress variations throughout its life. This would result in the possibility of fatigue cracking in its members. Cracks in these structures usually initiate around welded areas, then grow progressively from the heat-affected zone to base metal through the thickness of the tubular members. Therefore, fatigue life improvement of offshore structures is of great importance. In this paper, structural analysis of an offshore platform is carried out and the critical joint is specified. The welding process is simulated and the residual stresses due to the welding are determined. Experimental residual stress measurement is carried... 

Protein fibrillation process (e.g., from amyloid beta (Aβ) and α-synuclein) is the main cause of several catastrophic neurodegenerative diseases such as Alzheimer's and Parkinson diseases. During the past few decades, nanoparticles (NPs) were recognized as one of the most promising tools for inhibiting the progress of the disease by controlling the fibrillation kinetic process; for instance, gold NPs have a strong capability to inhibit Aβ fibrillations. It is now well understood that a layer of biomolecules would cover the surface of NPs (so called "protein corona") upon the interaction of NPs with protein sources. Due to the fact that the biological species (e.g., cells and amyloidal...