Equivalent forms of Dirac equations in curved spacetimes and generalized de Broglie relations

One may ask whether the relations between energy and frequency and between momentum and wave vector, introduced for matter waves by de Broglie, are rigorously valid in the presence of gravity. In this paper, we show this to be true for Dirac equations in a background of gravitational and electromagnetic fields. We first transform any Dirac equation into an equivalent canonical form, sometimes used in particular cases to solve Dirac equations in a curved spacetime. This canonical form is needed to apply the Whitham Lagrangian method. The latter method, unlike the WKB method, places no restriction on the magnitude of Planck's constant to obtain wave packets, and furthermore preserves the symmetries of the Dirac Lagrangian. We show using canonical Dirac fields in a curved spacetime, that the probability current has a Gordon decomposition into a convection current and a spin current, and that the spin current vanishes in the Whitham approximation, which explains the negligible effect of spin on wave packet solutions, independent of the size of Planck's constant. We further discuss the classical-quantum correspondence in a curved spacetime based on both Lagrangian and Hamiltonian formulations of the Whitham equations. We show that the generalized de Broglie relations in a curved spacetime are a direct consequence of Whitham's Lagrangian method, and not just a physical hypothesis as introduced by Einstein and de Broglie, and by many quantum mechanics textbooks.Comment: PDF, 32 pages in referee format. Added significant material on canonical forms of Dirac equations. Simplified Theorem 1 for normal Dirac equations. Added section on Gordon decomposition of the probability current. Encapsulated main results in the statement of Theorem

Design and operation of a Rayleigh Ohnesorge Jetting Extensional Rheometer (ROJER) to study extensional properties of low viscosity polymer solutions

The Rayleigh Ohnesorge Jetting Extensional Rheometer (ROJER) enables measurement of very short relaxation times of low viscosity complex fluids such as those encountered in ink-jet printing and spraying applications. This paper focuses on the design and operation of the ROJER. The performance of two nozzle designs are compared using Newtonian fluids alongside a study using computational fluid dynamics (CFD). Subsequently a disposable nozzle is developed that overcomes issues of blockage and cleaning. The operability of this design is subject to a focused study where low viscosity polymer solutions are characterised. The test fluid materials are ethyl hydroxy-ethyl cellulose (EHEC) and poly ethylene oxide (PEO) mixed with water/glycerol solutions. Results obtained by the disposable nozzle are encouraging, paving the way for a more cost-efficient and robust ROJER setup

Cutting Edge Geometry Effect on Plastic Deformation of Titanium Alloy

The paper presents experimental studies of ОТ4 titanium alloy machining with cutting edges of various geometry parameters. Experiments were performed at a low speed by the scheme of free cutting. Intensity of plastic shear strain was set for defining of cutting edge geometry effect on machining. Images of chip formed are shown. Estimation of strain magnitude was accomplished with digital image correlation method. Effect of rake angle and cutting edge angle has been studied. Depth of deformed layer and the area of the plastic strain is determine. Results showed that increasing the angle of the cutting edge inclination results in a change the mechanism of chip formation

Biochemical composition and calorie content of pollock <i>Theragra chalcogramm</i>a in the Okhotsk Sea

Walleye pollock tissues include 18.5 % of dry matter, on average. Lipids are 0.7 % of the pollock wet weight, proteins - 15.3 %, carbohydrates - 0.6 %, and ash - 1.3 %. Mean calorie content of its tissues is 940 cal/g for the raw material and 5080 cal/g for the dry matter. Portion of dry matter in its gonads is 14.9-28.0 % for females and 14.5-17.0 % for males; lipids content in the gonads is 0.9-3.0/1.3-1.8 % for females/males and proteins content is 10.7-13.4/10.2-21.5 %, respectively; calorie content of the gonads is 702-1537/4426-5482 cal/g for the raw/dry matter of females and 760-960/4952-5641 cal/g for the raw/dry matter of males. The pollock liver contains 42.2-62.2/34.4-62.4 % of dry matter for females/males, including 25.6-44.5/16.6-41.3 % of lipids and 6.3-9.8/8.1-12.3 % of proteins, respectively, with calorie content 2918-4601/6370-7395 cal/g for the raw/dry matter of females and 2291-4357/6392-7492 cal/g for the raw/dry matter of males. The calorie content of the liver tissue is much lower for the juveniles: 963/2045 cal/g for the raw/dry matter. The pollock faeces contain 15.0-18.4 % of dry matter, in dependence on the fish size, including 1.1-1.6 % of lipids, 1.8-3.8 % of proteins, and 0.9-1.4 % of carbohydrates; their calorie content is rather stable for the raw material (308-362 cal/g) but the calorie content of the dry faecal matter depends strongly on the fish size and varies from 259 to 2377 cal/g. The muscle tissue of pollock accumulates 56.5-93.9 % of the total energy content of its body, the gonads - 0.9-26.6 % for females and 0.4-7.3 % for males, the liver - 7.9-27.2 % for females and 5.7-26.9 % for males, i.e. energy accumulation in gonads and liver of females is higher than in these organs of males. Maximum loss of energy (15-30 %) is observed during the spawning, on the transition from stage 5 to stage 6 of maturity. The total accumulated energy during the pollock growth from juvenile fish ( 60 cm) is on average 1964 kcal for females and 1465 kcal for males, the difference is caused by higher energy needs for oogenesis, as compared with spermatogenesis

Accelerated apoptotic death and <i>in vivo</i> turnover of erythrocytes in mice lacking functional mitogen- and stress-activated kinase MSK1/2

The mitogen- and stress-activated kinase MSK1/2 plays a decisive role in apoptosis. In analogy to apoptosis of nucleated cells, suicidal erythrocyte death called eryptosis is characterized by cell shrinkage and cell membrane scrambling leading to phosphatidylserine (PS) externalization. Here, we explored whether MSK1/2 participates in the regulation of eryptosis. To this end, erythrocytes were isolated from mice lacking functional MSK1/2 (msk−/−) and corresponding wild-type mice (msk+/+). Blood count, hematocrit, hemoglobin concentration and mean erythrocyte volume were similar in both msk−/− and msk+/+ mice, but reticulocyte count was significantly increased in msk−/− mice. Cell membrane PS exposure was similar in untreated msk−/− and msk+/+ erythrocytes, but was enhanced by pathophysiological cell stressors ex vivo such as hyperosmotic shock or energy depletion to significantly higher levels in msk−/− erythrocytes than in msk+/+ erythrocytes. Cell shrinkage following hyperosmotic shock and energy depletion, as well as hemolysis following decrease of extracellular osmolarity was more pronounced in msk−/− erythrocytes. The in vivo clearance of autologously-infused CFSE-labeled erythrocytes from circulating blood was faster in msk−/− mice. The spleens from msk−/− mice contained a significantly greater number of PS-exposing erythrocytes than spleens from msk+/+ mice. The present observations point to accelerated eryptosis and subsequent clearance of erythrocytes leading to enhanced erythrocyte turnover in MSK1/2-deficient mice

HER2 and p95HER2 differentially regulate miRNA expression in MCF-7 breast cancer cells and downregulate MYB proteins through miR-221/222 and miR-503

Mecanismes de la malaltia; Càncer de mamaMecanismos de la enfermedad; Cáncer de mamaDisease Mechanisms; Breast CancerThe HER2 oncogene and its truncated form p95HER2 play central roles in breast cancer. Here, we show that although HER2 and p95HER2 generally elicit qualitatively similar changes in miRNA profile in MCF-7 breast cancer cells, a subset of changes are distinct and p95HER2 shifts the miRNA profile towards the basal breast cancer subtype. High-throughput miRNA profiling was carried out 15, 36 and 60 h after HER2 or p95HER2 expression and central hits validated by RT-qPCR. miRNAs strongly regulated by p95HER2 yet not by HER2, included miR-221, miR-222, miR-503, miR-29a, miR-149, miR-196 and miR-361. Estrogen receptor-α (ESR1) expression was essentially ablated by p95HER2 expression, in a manner recapitulated by miR-221/-222 mimics. c-Myb family transcription factors MYB and MYBL1, but not MYBL2, were downregulated by p95HER2 and by miR-503 or miR-221/-222 mimics. MYBL1 3′UTR inhibition by miR-221/222 was lost by deletion of a single putative miR-221/222 binding sites. p95HER2 expression, or knockdown of either MYB protein, elicited upregulation of tissue inhibitor of matrix metalloprotease-2 (TIMP2). miR-221/222 and -503 mimics increased, and TIMP2 knockdown decreased, cell migration and invasion. A similar pathway was operational in T47D- and SKBr-3 cells. This work reveals important differences between HER2- and p95HER2- mediated miRNA changes in breast cancer cells, provides novel mechanistic insight into regulation of MYB family transcription factors by p95HER2, and points to a role for a miR-221/222– MYB family–TIMP2 axis in regulation of motility in breast cancer cells.This work was supported by the Danish Council for Independent Research (grants no. 12-126942 and 12-127290 to SFP), by the Hartmann foundation (SFP), Fondation Juchum (SFP), Kirsten og Freddy Johansens Fond (SFP), the Breast Cancer Research Foundation (BCRF-17-008) (JA), Instituto de Salud Carlos III (PI16/00253) (JA) and the Harboe foundation (SFP). Katrine Franklin Mark is gratefully acknowledged for excellent technical assistance. We are grateful to Pascal Pineau from Institut Pasteur, France for the MYBL1 3′UTR/psiCHECK2 construct

Thromboembolic risk factors and predictors of left atrial appendage thrombosis in Far North patients with nonvalvular atrial fibrillation

Aim. To analyze thromboembolic risk factors and identify additional predictors of left atrial appendage (LAA) thrombosis, which are not included in the CHA2DS2VASc scale, in long-term Far North residents with nonvalvular atrial fibrillation (AF).Material and methods. The study included 162 patients (men, 108; women, 54; mean age, 55,3±8,7 years) with non-valvular AF, living in the Far North, and 684 patients (men, 408; women, 276; mean age, 56,9±9,3 years), living in the temperate latitudes, hospitalized for catheter ablation. All patients underwent transthoracic and transesophageal echocardiography. According to transesophageal echocardiography, Far North patients were divided into two groups: group 1 — 21 patients with LAA thrombosis, group 2 — 141 patients without LAA thrombosis.Results. Compared to patients living in the temperate latitudes, Far North patients were younger (p=0,021) and were more likely to have type 2 diabetes (14,2% vs 8,3%, p=0,022), class ³II obesity (29,6% vs 21,1%, p=0,019), persistent AF(47,5% vs 33,2%, p=0,0019), LAA thrombosis (13% vs 6,6%, p=0,006), and severe structural and functional cardiac abnormalities (biatrial and right ventricular enlargement, lower left ventricular ejection fraction). In Far North patients, using logistic regression, independent predictors of LAA thrombosis were identified: an increase in left ventricular mass index (odds ratio (OR), 1,029; 95% confidence interval (CI), 1,011-1,048; p=0,001), persistent AF (OR, 3,521; 95% CI, 1,050-11,800; p=0,041).Conclusion. In Far North patients with nonvalvular AF, scheduled for catheter ablation, compared with patients from temperate latitudes, with a similar profile of cardiovascular diseases at a younger age, type 2 diabetes, grade ³II obesity, persistent AF, and LAA thrombosis were more common. The presence of persistent AF and an increase in left ventricular mass index are independent predictors of LAA thrombosis in Far North patients with nonvalvular AF