Coupled fixed point theorems for contractions in fuzzy metric spaces

In the present work, we prove a coupled fixed point theorem for contractive mappings in complete fuzzy metric spaces.     

A study on monotone self-dual Boolean functions

This paper shows that monotone self-dual Boolean functions in irredundant disjuntive normal form (IDNF) do not have more variables than disjuncts. Monotone self-dual Boolean functions in IDNF with the same number of variables and disjuncts are examined. An algorithm is proposed to test whether a monotone Boolean function in IDNF with n variables and n disjuncts is self-dual. The runtime of the algorithm is O(n³).     

Generalized Lucas polynomials and relationships between the Fibonacci polynomials and Lucas polynomials

In this article, we find elements of the Lucas polynomials by using two matrices. We extend the study to the n-step Lucas polynomials. Then the Lucas polynomials and their relationship are generalized in the paper. Furthermore, we give relationships between the Fibonacci polynomials and the Lucas polynomials.     

Remarks on the Formulation of the Cosmological Constant/Dark Energy Problems

Associated with the cosmic acceleration are the old and new cosmological constant problems, recently put into the more general context of the dark energy problem. In broad terms, the old problem is related to an unexpected order of magnitude of this component while the new problem is related to this magnitude being of the same order of the matter energy density during the present epoch of cosmic evolution. Current plans to measure the equation of state or density parameters certainly constitute an important approach; however, as we discuss, this approach is faced with serious feasibility challenges and is limited in the type of conclusive answers it could provide. Therefore, is it really too early to seek actively for new tests and approaches to these problems? In view of the difficulty of this endeavor, we argue in this work that a good place to start is by questioning some of the assumptions underlying the formulation of these problems and finding new ways to put this questioning to the test. First, we calculate how much fine tuning the cosmic coincidence problem represents. Next, we discuss the potential of some cosmological probes such as weak gravitational lensing to identify novel tests to probe dark energy questions and assumptions and provide an example of consistency tests. Then, motivated by some theorems in General Relativity, we discuss if the full identification of the cosmological constant with vacuum energy is unquestionable. We discuss some implications of the simplest solution for the principles of General Relativity. Also, we point out the relevance of experiments at the interface of astrophysics and quantum field theory, such as the Casimir effect in gravitational and cosmological contexts. We conclude that challenging some of the assumptions underlying the cosmological constant problems and putting them to the test may prove useful and necessary to make progress on these questions.     

Reinforcement of natural rubber/high density polyethylene blends with electron beam irradiated liquid natural rubber-coated rice husk

Coating of rice husk (RH) surface with liquid natural rubber (LNR) and exposure to electron beam irradiation in air were studied. FTIR analysis on the LNR-coated RH (RHR) exposed to electron beam (EB) showed a decrease in the double bonds and an increase in hydroxyl and hydrogen bonded carbonyl groups arising from the chemical interaction between the active groups on RH surface with LNR. The scanning electron micrograph showed that the LNR formed a coating on the RH particles which transformed to a fine and clear fibrous layer at 20 kGy irradiation. The LNR film appeared as patches at 50 kGy irradiation due to degradation of rubber. Composites of natural rubber (NR)/high density polyethylene (HDPE)/RHR showed an optimum at 20–30 kGy dosage with the maximum stress, tensile modulus and impact strength of 6.5, 79 and 13.2 kJ/m², respectively. The interfacial interaction between the modified RH and TPNR matrix had improved on exposure of RHR to e-beam at 20–30 kGy dosage.     

Synthesis of branched carbasugars via photooxygenation and manganese(III) acetate free radical cyclization

Transformation of cyclohexa-1,3- and 1,4-dienes to carbasugars is described. Photooxygenation of dienes gave bicyclic endoperoxides, which were reduced with thiourea to the corresponding 1,4-diols with cis-configuration. Lactonization of the remaining double bond by oxidative addition of acetic acid to the double bond in the presence of Mn(OAc)₃ followed by lactone ring-opening reaction gave the target branched carbasugars.     

A modulated dsc study on the in situ polymerization of cyclic butylene terephthalate oligomers

The polymerization of a cyclic butylene terephthalate (CBT) oligomer was studied as a function of temperature (T=200 and 260°C, respectively) by modulated DSC (MDSC). The first heating was followed by cooling after various holding times (5, 15 and 30 min) prior to the second heating which ended always at T=260°C. This allowed us to study the crystallization and melting behavior of the resulting polybutylene terephthalate (PBT), as well. In contrary to the usual belief, the CBT polymerization is exothermic and the related process is superimposed to that of the CBT melting. The melting behavior of the PBT was affected by the polymerization mode (performed below or above the melting temperature of the PBT product) of the CBT. Annealing above the melting temperature of PBT yielded a product featuring double melting. This was attributed to the presence of crystallites with different degrees of perfection. The crystals perfection which occurred via recrystallization/remelting was manifested by a pronounced exothermic peak in the non-reversing trace.     

Quantum mechanical/molecular mechanical studies on spectral tuning mechanisms of visual pigments and other photoactive proteins

The protein environments surrounding the retinal tune electronic absorption maximum from 350 to 630 nm. Hybrid quantum mechanical/molecular mechanical (QM/MM) methods can be used in calculating excitation energies of retinal in its native protein environments and in studying the molecular basis of spectral tuning. We hereby review recent QM/MM results on the phototransduction of bovine rhodopsin, bacteriorhodopsin, sensory rhodopsin II, nonretinal photoactive yellow protein and their mutants.     

The hydrolytic effect of moisture and hygrothermal aging on poly(butylene succinate)/organo-montmorillonite nanocomposites

The study of hydrolysis on biodegradable poly(butylene succinate) (PBS) is essential to predict the materials properties in a humid environment. In this study, PBS nanocomposites were exposed to different conditions of relative humidity (RH) and temperature. The moisture uptake increased with organo-montmorillonite (OMMT) loading and the RH of the testing environment. The exposure of PBS and the nanocomposites to a humid environment caused changes in the mechanical properties. The hydrolytic degradation becomes more pronounced upon hygrothermal aging at high temperature, whereby premature failure occurred. PBS nanocomposites were found to exhibit a better hydrolytic stability than neat PBS. The degradation was evaluated through Fourier transform infrared (FTIR) spectroscopy and gel permeation chromatography (GPC). A drastic reduction in the molecular weight of PBS has revealed the occurrence of degradation after exposure to moisture and heat. This has led to an alteration of the thermal behavior as investigated using differential scanning calorimetry (DSC).