Inequalities for E k(X,Y) when the marginals are fixed

When k(x, y) is a quasi-monotone function and the random variables X and Y have fixed distributions, it is shown under some further mild conditions that k(X, Y) is a monotone functional of the joint distribution function of X and Y. Its infimum and supremum are both attained and correspond to explicitly described joint distribution functions.Research supported by the Air Force Office of Scientific Research under Grant AFOSR-75-2796Research supported by the National Science Foundation     

On the Partial Sums of a Fourier Series

We give sharp lower estimates for the partial sums of the Fourier series

Are semi-numerical methods an effective tool for locating periodic orbits in 3D potentials?

A semi-numerical method is used in order to locate the position and calculate the period of periodic orbits in a 3D composite bisymmetrical potential, in a number of resonant cases. The potential consists of a 3D harmonic oscillator and a Plummer sphere. The outcomes are compared with results found using the numerical integration of the equations of motion and the agreement is very good. This agreement strongly suggests, that semi-numerical methods can be used in order to obtain fast and reliable results regarding the position and period of the periodic orbits in 3D composite potentials with a harmonic oscillator part and different kinds of perturbations. Comparison with other methods of obtaining 3D periodic orbits is discussed.     

Remarks on some completely monotonic functions

Applying the Euler-Maclaurin summation formula, we obtain upper and lower polynomial bounds for the function , x>0, with coefficients the Bernoulli numbers Bk. This enables us to give simpler proofs of some results of H. Alzer and F. Qi et al., concerning complete monotonicity of certain functions involving the gamma function Γ(x), the psi function ψ(x) and the polygamma functions ψ(n)(x), n=1,2,… .     

Reactivity of 2‐Methyl‐4H‐3,1‐benzoxazin‐4‐ones and 2‐Methyl‐4H‐pyrido[2,3‐d][1,3]oxazin‐4‐one under Microwave Irradiation Conditions

The reactivity of variably substituted 2‐methyl‐4H‐3,1‐benzoxazin‐4‐ones and 2‐methyl‐4H‐pyrido[2,3‐d][1,3]oxazin‐4‐one towards carbon and oxygen nucleophiles under microwave irradiation conditions was investigated. Optimization of the reaction conditions of oxazinones with carbon nucleophiles led to the synthesis of a series of 4‐hydroxy‐quinolin‐2‐ones and 4‐hydroxy‐1,8‐naphthyridin‐2‐ones in high yields, whereas reaction with a variety of alcohols proceeded smoothly to the formation of the corresponding N‐acetyl‐anthranilates and nicotinates.     

Phase transitions and electrical properties of As2Te3

This study identifies and characterizes the phase transitions induced thermally in bulk amorphous and crystalline As₂Te₃. In addition, it examines the nature and the electrical properties of the various As₂Te₃ phases, and attempts to correlate the memory electrical switching exhibited by these materials with their phase transitions.     

Carbon Nanostructures Derived through Hypergolic Reaction of Conductive Polymers with Fuming Nitric Acid at Ambient Conditions

Hypergolic systems rely on organic fuel and a powerful oxidizer that spontaneously ignites upon contact without any external ignition source. Although their main utilization pertains to rocket fuels and propellants, it is only recently that hypergolics has been established from our group as a new general method for the synthesis of different morphologies of carbon nanostructures depending on the hypergolic pair (organic fuel-oxidizer). In search of new pairs, the hypergolic mixture described here contains polyaniline as the organic source of carbon and fuming nitric acid as strong oxidizer. Specifically, the two reagents react rapidly and spontaneously upon contact at ambient conditions to afford carbon nanosheets. Further liquid-phase exfoliation of the nanosheets in dimethylformamide results in dispersed single layers exhibiting strong Tyndall effect. The method can be extended to other conductive polymers, such as polythiophene and polypyrrole, leading to the formation of different type carbon nanostructures (e.g., photolumincent carbon dots). Apart from being a new synthesis pathway towards carbon nanomaterials and a new type of reaction for conductive polymers, the present hypergolic pairs also provide a novel set of rocket bipropellants based on conductive polymers.     

Investigating the nature of motion in 3D perturbed elliptic oscillators displaying exact periodic orbits

We study the nature of motion in a 3D potential composed of perturbed elliptic oscillators. Our technique is to use the results obtained from the 2D potential in order to find the initial conditions generating regular or chaotic orbits in the 3D potential. Both 2D and 3D potentials display exact periodic orbits together with extended chaotic regions. Numerical experiments suggest that the degree of chaos increases rapidly as the energy of the test particle increases. About 97?% of the phase plane of the 2D system is covered by chaotic orbits for large energies. The regular or chaotic character of the 2D orbits is checked using the S(c) dynamical spectrum, while for the 3D potential we use the S(c) spectrum, along with the P(f) spectral method. Comparison with other dynamical indicators shows that the S(c) spectrum gives fast and reliable information about the character of motion.     

Spectroscopic and catalytic studies of lipases in ternary hexane-1-propanol-water surfactantless microemulsion systems

A series of water-in-oil microemulsion systems formulated without surfactant were used to solubilize lipases from Rhizomucor miehei and Candida antarctica B. The effect of the system's composition on the velocity of enzymic reactions was investigated following a model esterification reaction. The interaction between enzymes and the microemulsion environment was studied by steady state fluorescence spectroscopy. The site of localization of the enzyme within the different microdomains of the dispersed phase was investigated by applying the fluorescence energy transfer technique. To determine the properties of the interface between water and organic solvent of the surfactantless microemulsion systems the Electron Paramagnetic Resonance (EPR) spectroscopic technique was applied. The results indicated that even at low water content, water-rich structures are formed. This was confirmed by conductivity measurements. By the addition of enzyme it was observed that when the aqueous phase of the surfactantless microemulsion systems exceeds 2% (v/v) the enzyme retains its catalytic activity, as it is located within the water pools that protect it from the organic solvent. These confined water phases show a propanol rich interface with hexane and their structure depends on the system's composition.     

A refinement of Vietoris' inequality for sine polynomials

Let where In 1958, Vietoris proved that σ_n (x) is positive for all n ≥ 1 and x ∈ (0, π). We establish the following refinement. The inequalities hold for all natural numbers n and real numbers n ≥ 1 and x ∈ (0, π) if and only if