Perturbation Method for Particle-like Solutions of the Einstein–Dirac Equations

The aim of this work is to prove by a perturbation method the existence of solutions of the coupled Einstein–Dirac equations for a static, spherically symmetric system of two fermions in a singlet spinor state. We relate the solutions of our equations to those of the nonlinear Choquard equation and we show that the nondegenerate solution of Choquard’s equation generates solutions of the Einstein–Dirac equations.     

Synthesis and Biological Evaluation of Some New N1‐[4‐(4‐Chlorophenylsulfonyl)benzoyl]‐N 4‐(aryl)‐thiosemicarbazides and Products of Their Cyclization

In the present study, new 1,2,4‐triazoles, 1,3,4‐thiadiazoles, and acylthiosemicarbaz‐ides derived from 4‐(4‐chlorophenylsulfonyl)benzoic acid hydrazide were synthesized and screened for their antimicrobial and analgesic activities. Acylthiosemicarbazides 2–4 were synthesized by a reaction of 4‐(4‐chlorophenyl‐sulfonyl)benzoic acid hydrazide 1 with different arylisothiocyanates.4,5‐Disubstituted‐2,4‐dihydro‐3H‐1,2,4‐triazol‐3‐thiones 5–7 and 2,5‐disubstituted‐1,3,4‐thiadiazoles 8–10 were obtained by dehydrative cyclization of corresponding acylthiosemicarbazide derivatives 2–4 in basic media (8% aqueous sodium hydroxide) and in acidic media (sulfuric acid or phosphorous oxychloride), respectively. The structures of the newly synthesized compounds have been confirmed on the basis of elemental analysis and spectral studies (IR, ¹H NMR, ¹³C NMR, MS). Their antimicrobial activities against some bacteria and yeasts were investigated. The analgesic activity of all compounds was performed with two pharmacological tests: the writhing test induced with acetic acid and hot‐plate test. The results showed that triazole 7 had the best antimicrobial activity against Bacillus cereus. In the chemical stimulus test, triazoles 6 and 7 were the most active compounds whereas in the hot‐plate test thiadiazoles 9 and 10 exhibited the highest analgesic activity.     

An inventory-transportation system with stochastic demand

We study a logistic system in which a supplier has to deliver a set of products to a set of retailers to face a stochastic demand over a given time horizon. The transportation from the supplier to each retailer can be performed either directly, by expensive and fast vehicles, or through an intermediate depot, by less expensive but slower vehicles. At most one time period is required in the former case, while two time periods are needed in the latter case. A variable transportation cost is charged in the former case, while a fixed transportation cost per journey is charged in the latter case. An inventory cost is charged at the intermediate depot. The problem is to determine, for each time period and for each product, the quantity to send from the supplier to the depot, from the depot to each retailer and from the supplier to each retailer, in order to minimize the total expected cost. We first show that the classical benchmark policy, in which the demand of each product at each retailer is set equal to the average demand, can give a solution which is infinitely worse with respect to the optimal solution. Then, we propose two classes of policies to solve this problem. The first class, referred to as Horizon Policies, is composed of policies which require the solution of the overall problem over the time horizon. The second class, referred to as Reoptimization Policies, is composed of a myopic policy and several rolling-horizon policies in which the problem is reoptimized at each time period, once the demand of the time period is revealed. We evaluate the performance of each policy dynamically, by using Monte Carlo Simulation.     

Continuous‐wave optical parametric oscillator based infrared spectroscopy for sensitive molecular gas sensing

Over the past 10 years, with the advent of new crystals designs and a new generation of pump lasers, continuous‐wave (cw) optical parametric oscillators (OPOs) have developed into mature monochromatic light sources. Nowadays, cw OPOs can fulfill a wide variety of criteria for sensitive molecular gas sensing. It can access the mid‐infrared wavelength region, where many molecules have their fundamental rotational‐vibrational transitions, with high power. This high power combined with wide wavelength tuning and narrow linewidth creates excellent conditions for sensitive, high‐resolution spectroscopy. OPOs combined with robust methods, such as photoacoustic spectroscopy and cavity‐enhanced spectroscopy, are well suited for field measurements and remote‐sensing applications. The wide tunability of cw OPOs allows detection of larger molecules with broad absorption band structures, and its fast scanning capabilities allow rapid detection of trace gases, the latter is a demand for life‐science applications. After a short introduction about the physical principle of cw OPOs, with its most recent physical developments, this review focuses on sensitive molecular gas sensing with a variety of spectroscopic applications in atmospheric and life sciences.     

Luciferase‐Induced Photouncaging: Bioluminolysis

Bioluminescence resonance energy transfer (BRET) has been widely used for studying dynamic processes in biological systems such as protein–protein interactions and other signaling events. Aside from acting as a reporter, BRET can also turn on functions in living systems. Herein, we report the application of BRET to performing a biorthogonal reaction in living cells; namely, releasing functional molecules through energy transfer to a coumarin molecule, a process termed bioluminolysis. An efficient BRET from Nanoluc‐Halotag chimera protein (H‐Luc) to a coumarin substrate yields the excited state of coumarin, which in turn triggers hydrolysis to uncage a target molecule. Compared to the conventional methods, this novel uncaging system requires no external light source and shows fast kinetics (t_1/2<2 min). We applied this BRET uncaging system to release a potent kinase inhibitor, ibrutinib, in living cells, highlighting its broad utility in controlling the supply of bioactive small molecules in vivo.     

Rational Design and Development of Anisotropic and Mechanically Strong Gelatin‐Based Stress Relaxing Hydrogels for Osteogenic/Chondrogenic Differentiation

Rational design and development of tailorable simple synthesis process remains a centerpiece of investigational efforts toward engineering advanced hydrogels. In this study, a green and scalable synthesis approach is developed to formulate a set of gelatin‐based macroporous hybrid hydrogels. This approach consists of four sequential steps starting from liquid‐phase pre‐crosslinking/grafting, unidirectional freezing, freeze‐drying, and finally post‐curing process. The chemical crosslinking mainly involves between epoxy groups of functionalized polyethylene glycol and functional groups of gelatin both in liquid and solid state. Importantly, this approach allows to accommodate different polymers, chitosan or hydroxyethyl cellulose, under identical benign condition. Structural and mechanical anisotropy can be tuned by the selection of polymer constituents. Overall, all hydrogels show suitable structural stability, good swellability, high porosity and pore interconnectivity, and maintenance of mechanical integrity during 3‐week‐long hydrolytic degradation. Under compression, hydrogels exhibit robust mechanical properties with nonlinear elasticity and stress‐relaxation behavior and show no sign of mechanical failure under repeated compression at 50% deformation. Biological experiment with human bone marrow mesenchymal stromal cells (hMSCs) reveals that hydrogels are biocompatible, and their physicomechanical properties are suitable to support cells growth, and osteogenic/chondrogenic differentiation, demonstrating their potential application for bone and cartilage regenerative medicine toward clinically relevant endpoints.     

Dynamic response of rocking cracked masonry walls

The behaviour of masonry constructions results to be very far from the one characterizing ductile structures. In masonry constructions, the seismic action activates a rocking motion rather than a dissipating mechanism. A strength resource of masonry structures, properly reinforced in order to avoid early local failures, consists in exhibiting rocking behaviour, until a failure condition is attained. Aim of the paper is to investigate the dynamic behaviour of masonry single storey walls, according to Housner’s studies and innovatively introducing the effect of diagonal cracks developing from the toes of the piers and shown by typical post-earthquake cracking patterns. The proposed procedure can be easily applied to the case of multi-storey regular masonry walls with openings representing the main resistant structural components of a masonry building. Starting from the evaluation of the incipient rocking acceleration of the system, the free and forced motions of the wall are examined. In the paper, according to the classical Housner’s approach, the energy dissipation occurring during the impact is modelled. Finally, a numerical application, considering a simple constant horizontal acceleration impulse of given duration has been carried out.