Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators

In this paper, by using the method of separation of variables, we obtain eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator defined via fractional Caputo derivatives. The solutions are expressed using the Mittag-Leffler function and we show some graphical representations for some parameters. A family of fundamental solutions of the corresponding fractional Dirac operator is also obtained. Particular cases are considered in both cases.

D. Martini Lutheri Commentarium in Epistolam S. Pauli ad Galatas /

Mode of access: Internet.

Topological massive Dirac edge modes and long-range superconducting Hamiltonians

We discover novel topological effects in the one-dimensional Kitaev chain modified by long-range Hamiltonian deformations in the hopping and pairing terms. This class of models display symmetry-protected topological order measured by the Berry/Zak phase of the lower-band eigenvector and the winding number of the Hamiltonians. For exponentially decaying hopping amplitudes, the topological sector can be significantly augmented as the penetration length increases, something experimentally achievable. For power-law decaying superconducting pairings, the massless Majorana modes at the edges get paired together into a massive nonlocal Dirac fermion localized at both edges of the chain: a new topological quasiparticle that we call topological massive Dirac fermion. This topological phase has fractional topological numbers as a consequence of the long-range couplings. Possible applications to current experimental setups and topological quantum computation are also discussed.

Detecting KaiC Phosphorylation Rhythms of the Cyanobacterial Circadian Oscillator In Vitro and In Vivo

The central oscillator of the cyanobacterial circadian clock is unique in the biochemical simplicity of its components and the robustness of the oscillation. The oscillator is composed of three cyanobacterial proteins: KaiA, KaiB, and KaiC. If very pure preparations of these three proteins are mixed in a test tube in the right proportions and with ATP and MgCl2, the phosphorylation states of KaiC will oscillate with a circadian period, and these states can be analyzed simply by SDS-PAGE. The purity of the proteins is critical for obtaining robust oscillation. Contaminating proteases will destroy oscillation by degradation of Kai proteins, and ATPases will attenuate robustness by consumption of ATP. Here, we provide a detailed protocol to obtain pure recombinant proteins from Escherichia coli to construct a robust cyanobacterial circadian oscillator in vitro. In addition, we present a protocol that facilitates analysis of phosphorylation states of KaiC and other phosphorylated proteins from in vivo samples.

Epistolæ Pauli et aliorum apostolorum ad Græcam veritatem castigatæ, & per Reuerendissimum Dominum Dominu[m] Thomam de Vio, ... iuxta sensum literalem enarratæ : quibus accesserunt Actus Apostolorum commentariis eiusdem illustrati / [Commentariorum Thoma

Omnia accuratiori cura quàm antea excusa

Practica cancellariæ apostolicæ cum stylo & formis in Romana Curia vsitatis, excerpta nuper ex memorabilibus D. Hier. Pauli ... : his & in fine adiectum est Prouinciale omnium Ecclesiarum cathedralium vniuersi orbis ...

Marca tip. del librero Vincent de Portonariis en ambas port. (Baudrier. V, p. 404, n. 6)

The quantum time-dependent harmonic oscillator

La presente tesi si propone di mostrare che l’oscillatore armonico quantistico dipendente dal tempo è un sistema risolvibile in maniera esatta. La trattazione è articolata in tre capitoli: nel primo viene richiamata la teoria dell’oscillatore armonico quantistico indipendente dal tempo, al fine di recuperare i concetti e le metodologie che sono comuni anche alla sua controparte dipendente dal tempo. Nel secondo capitolo viene fornita una breve introduzione alla teoria degli operatori invarianti dipendenti dal tempo, di cui ci interessa la loro relazione con le soluzioni dell’equazione di Schrödinger. Infine, nel terzo capitolo viene presentato il problema dell’oscillatore armonico quantistico dipendente dal tempo e discussa la sua soluzione esatta. In aggiunta se ne individuano gli stati coerenti.

Equazione di Dirac in grafene con deformazioni di reticolo

In questa tesi si sono analizzate le principali conseguenze dovute alle deformazioni nel reticolo cristallino del grafene. Si è fatta innanzitutto, una descrizione generale della struttura cristallina, seguita dal caso specifico del reticolo esagonale del grafene. Si è poi, passati alla struttura elettronica studiata in approssimazione di legame forte tramite il formalismo della seconda quantizzazione, arrivando a descrivere la particolare struttura a bande coniche del grafene, dove i portatori di carica, detti quasiparticelle, sono ben descritti dall'equazione di Dirac. Si sono, in seguito, introdotte le deformazioni del reticolo e i metodi per ottenerle, arrivando ad ampliare l'equazione di Dirac, inserendo in essa gli effetti dei potenziali, pseudo-vettore e scalare, indotti dalla deformazione. Questi potenziali indotti portano con loro alcune conseguenze, si sono analizzate in particolare quelle sulla distribuzione di carica, con particolare attenzione agli effetti di confinamento, e quelle sul trasporto di carica, in particolare riguardanti il filtraggio di valle.

Treadmill Training Increases Sirt-1 And Pgc-1 α Protein Levels And Ampk Phosphorylation In Quadriceps Of Middle-aged Rats In An Intensity-dependent Manner.

The present study investigated the effects of running at 0.8 or 1.2 km/h on inflammatory proteins (i.e., protein levels of TNF- α , IL-1 β , and NF- κ B) and metabolic proteins (i.e., protein levels of SIRT-1 and PGC-1 α , and AMPK phosphorylation) in quadriceps of rats. Male Wistar rats at 3 (young) and 18 months (middle-aged rats) of age were divided into nonexercised (NE) and exercised at 0.8 or 1.2 km/h. The rats were trained on treadmill, 50 min per day, 5 days per week, during 8 weeks. Forty-eight hours after the last training session, muscles were removed, homogenized, and analyzed using biochemical and western blot techniques. Our results showed that: (a) running at 0.8 km/h decreased the inflammatory proteins and increased the metabolic proteins compared with NE rats; (b) these responses were lower for the inflammatory proteins and higher for the metabolic proteins in young rats compared with middle-aged rats; (c) running at 1.2 km/h decreased the inflammatory proteins and increased the metabolic proteins compared with 0.8 km/h; (d) these responses were similar between young and middle-aged rats when trained at 1.2 km. In summary, the age-related increases in inflammatory proteins, and the age-related declines in metabolic proteins can be reversed and largely improved by treadmill training.

Mechanical Properties And Fracture Dynamics Of Silicene Membranes.

As graphene has become one of the most important materials, there is renewed interest in other similar structures. One example is silicene, the silicon analogue of graphene. It shares some of the remarkable graphene properties, such as the Dirac cone, but presents some distinct ones, such as a pronounced structural buckling. We have investigated, through density functional based tight-binding (DFTB), as well as reactive molecular dynamics (using ReaxFF), the mechanical properties of suspended single-layer silicene. We calculated the elastic constants, analyzed the fracture patterns and edge reconstructions. We also addressed the stress distributions, unbuckling mechanisms and the fracture dependence on the temperature. We analysed the differences due to distinct edge morphologies, namely zigzag and armchair.

Hypothalamic S1p/s1pr1 Axis Controls Energy Homeostasis.

Sphingosine 1-phosphate receptor 1 (S1PR1) is a G-protein-coupled receptor for sphingosine-1-phosphate (S1P) that has a role in many physiological and pathophysiological processes. Here we show that the S1P/S1PR1 signalling pathway in hypothalamic neurons regulates energy homeostasis in rodents. We demonstrate that S1PR1 protein is highly enriched in hypothalamic POMC neurons of rats. Intracerebroventricular injections of the bioactive lipid, S1P, reduce food consumption and increase rat energy expenditure through persistent activation of STAT3 and the melanocortin system. Similarly, the selective disruption of hypothalamic S1PR1 increases food intake and reduces the respiratory exchange ratio. We further show that STAT3 controls S1PR1 expression in neurons via a positive feedback mechanism. Interestingly, several models of obesity and cancer anorexia display an imbalance of hypothalamic S1P/S1PR1/STAT3 axis, whereas pharmacological intervention ameliorates these phenotypes. Taken together, our data demonstrate that the neuronal S1P/S1PR1/STAT3 signalling axis plays a critical role in the control of energy homeostasis in rats.

Acute Exercise Decreases Trb3 Protein Levels In The Hypothalamus Of Obese Rats.

To evaluate the effects of acute exercise on the TRB3 protein levels and interaction between TRB3/Akt proteins in the hypothalamus of obese rats. In addition, we evaluated the relationship between TRB3 and endoplasmic reticulum stress (ER stress) and verified whether an acute exercise session is able to influence these processes. In the first part of the study, the rats were divided into three groups: control (lean) - fed with a standard rodent chow, DIO - fed with a high fat diet and DIO submitted to a swimming acute exercise protocol (DIO-EXE). In the second part of the study, we used other three groups: control (lean) receiving an intracerebroventricular (i.c.v.) infusion of vehicle, lean receiving an i.c.v. infusion of thapsigargin, and lean receiving an i.c.v infusion of thapsigargin and performing an acute exercise session. Four hours after the exercise session, the food intake was measured and the hypothalamus was dissected and separated for subsequent protein analysis by immunoblotting and Real Time PCR. The acute exercise session reduced the TRB3 protein levels, disrupted the interaction between TRB3/Akt proteins, increased the phosphorylation of Foxo1 and restored the anorexigenic effects of insulin in the hypothalamus of DIO rats. Interestingly, the suppressive effects of acute exercise on TRB3 protein levels may be related, at least in part, to the decrease of ER stress (evaluated though pancreatic ER kinase phosphorylation - pPERK and C/EBP homologous protein - CHOP protein levels) in the hypothalamus. In conclusion, the reduction of hypothalamic TRB3 protein levels mediated by exercise may be associated with the reduction of ER stress. These data provided a new mechanism by which an acute exercise session improves insulin sensitivity in hypothalamus and restores food intake control in obesity.

Undulatory Physical Resistance Training Program Increases Maximal Strength In Elderly Type 2 Diabetics.

To investigate the effects of a specific protocol of undulatory physical resistance training on maximal strength gains in elderly type 2 diabetics. The study included 48 subjects, aged between 60 and 85 years, of both genders. They were divided into two groups: Untrained Diabetic Elderly (n=19) with those who were not subjected to physical training and Trained Diabetic Elderly (n=29), with those who were subjected to undulatory physical resistance training. The participants were evaluated with several types of resistance training's equipment before and after training protocol, by test of one maximal repetition. The subjects were trained on undulatory resistance three times per week for a period of 16 weeks. The overload used in undulatory resistance training was equivalent to 50% of one maximal repetition and 70% of one maximal repetition, alternating weekly. Statistical analysis revealed significant differences (p<0.05) between pre-test and post-test over a period of 16 weeks. The average gains in strength were 43.20% (knee extension), 65.00% (knee flexion), 27.80% (supine sitting machine), 31.00% (rowing sitting), 43.90% (biceps pulley), and 21.10% (triceps pulley). Undulatory resistance training used with weekly different overloads was effective to provide significant gains in maximum strength in elderly type 2 diabetic individuals.

Eccentric Exercise Leads To Glial Activation But Not Apoptosis In Mice Spinal Cords.

The aim of this investigation was to evaluate the effects of 3 overtraining (OT) protocols on the glial activation and apoptosis in the spinal cords of mice. Rodents were divided into control (C; sedentary mice), overtrained by downhill running (OTR/down), overtrained by uphill running (OTR/up) and overtrained by running without inclination (OTR). The incremental load test, ambulation test, exhaustive test and functional behavioural assessment were used as performance evaluation parameters. 36 h after the exhaustive test, the dorsal and ventral parts of the lumbar spinal cord (L4-L6) were dissected for subsequent protein analysis by immunoblotting. The OT protocols led to similar responses of some performance parameters. The ventral glial fibrillary acidic protein (GFAP) protein levels were diminished in the OTR/up and OTR compared to CT and OTR/down groups. The ventral ionized calcium binding adaptor molecule 1 (Iba-1), and the dorsal GFAP and Iba-1 protein levels were increased in the OTR/down compared to the other groups. The ratio between the cleaved capase-3/caspase-3 and cleaved caspase-9/caspase-9 measured in the spinal cord were not sensitive to the OT protocols. In summary, the OTR/down activated the glial cells in the motor (i. e. Iba-1) and sensory (i. e. GFAP and Iba-1) neurons without leading to apoptosis.

Both accurate and precise gf-values for Fe II lines

We present a new set of oscillator strengths for 142 Fe II lines in the wavelength range 4000-8000 angstrom. Our gf-values are both accurate and precise, because each multiplet was globally normalized using laboratory data ( accuracy), while the relative gf-values of individual lines within a given multiplet were obtained from theoretical calculations ( precision). Our line list was tested with the Sun and high-resolution (R approximate to 10(5)), high-S/N (approximate to 700-900) Keck+HIRES spectra of the metal-poor stars HD 148816 and HD 140283, for which line-to-line scatter (sigma) in the iron abundances from Fe II lines as low as 0.03, 0.04, and 0.05 dex are found, respectively. For these three stars the standard error in the mean iron abundance from Fe II lines is negligible (sigma(mean) <= 0.01 dex). The mean solar iron abundance obtained using our gf-values and different model atmospheres is A(Fe) = 7.45(sigma = 0.02).