Structure of positive solution sets of semi-positone singular boundary value problems

In this paper we first obtain some results on the structure of positive solution sets of some differential boundary value problems. Then by using these results we obtain some existence and multiplicity results for positive solutions of differential boundary value problems. The method used to show the main results is that of global bifurcation theories.     

Coincidence theory for set-valued maps via compactness principles

A variety of coincidence type results are presented for set-valued maps on Hausdorff topological spaces. Our theory is based on coincidence results (in fact fixed point results) for compact maps.     

Compositional Changes in Sugarcane Bagasse on Low Temperature, Long-term Diluted Ammonia Treatment

Sugarcane bagasse is the major by-product of the sugar industry. It has a great potential for the production of biofuels and chemicals due to its considerable amount of cellulose and hemicellulose. In this study, we investigated a simple and economic pretreatment process using dilute ammonia for the storage of sugarcane bagasse. Sugarcane bagasse was stored in 0, 0.03, and 0.3% (w/w) ammonium hydroxide in a closed bottle for 40 days at 30 °C under atmospheric pressure without any agitation or circulation. Samples were taken every 10 days and analyzed for changes on lignin, cellulose, hemicellulose composition, ammonia concentration, and microbial counts. Biomass storage for 40 days at 0.3% ammonium hydroxide removed 46% of lignin and retained 100% cellulose and 73% hemicellulose.     

PET modulated fluorescent sensing from the BF2 chelated azadipyrromethene platform

A convergent building block synthesis has been applied to new off/on photoinduced electron transfer (PET) modulated fluorescent sensors which are based on a BF(2) chelated tetraarylazadipyrromethene platform and operate in the biomedically important red region of the visible spectrum. Incorporation of diethylamine and morpholine receptors facilitates off/on microenvironment polarity and pH sensing. Aqueous formulation and in vitro cellular imaging demonstrates their potential for intracellular sensing.     

Lefschetz fixed point theorems in generalized neighborhood extension spaces with respect to a map

We present several new Lefschetz fixed point results for compact self maps in new classes of spaces with respect to the map.     

Positive solutions of singular problems with sign changing Carathéodory nonlinearities depending on x′

We consider the singular boundary value problem for the differential equation x″+f(t,x,x′)=0 with the boundary conditions x(0)=0, w(x(T),x′(T))+?(x)=0. Here f is a Carathéodory function on which may by singular at the value x=0 of the phase variable x and f may change sign, w is a continuous function, and ? is a continuous nondecreasing functional on C⁰([0,T]). The existence of positive solutions on (0,T] in the classes AC¹([0,T]) and C⁰([0,T])∩AC¹_loc((0,T]) is considered. Existence results are proved by combining the method of lower and upper functions with Leray-Schauder degree theory.     

Correlation-Driven Magnetic Frustration and Insulating Behavior of TiF3

The halide perovskite TiF₃, renowned for its intricate interplay between structure, electronic correlations, magnetism, and thermal expansion, is investigated. Despite its simple structure, understanding its low-temperature magnetic behavior has been a challenge. Previous theories propose antiferromagnetic ordering. In contrast, experimental signatures for an ordered magnetic state are absent down to 10 K. The current study has successfully reevaluated the theoretical modeling of TiF₃, unveiling the significance of strong electronic correlations as the key driver for its insulating behavior and magnetic frustration. In addition, frequency-dependent optical reflectivity measurements exhibit clear signs of an insulating state. The analysis of the calculated magnetic data gives an antiferromagnetic exchange coupling with a net Weiss temperature of order 25 K as well as a magnetic response consistent with a S = 1/2 local moment per Ti³⁺. Yet, the system shows no susceptibility peak at this temperature scale and appears free of long-range antiferromagnetic order down to 1 K. Extending ab initio modeling of the material to larger unit cells shows a tendency for relaxing into a noncollinear magnetic ordering, with a shallow energy landscape between several magnetic ground states, promoting the status of this simple, nearly cubic perovskite structured material as a candidate spin liquid.