Hilbert Space of Probability Density Functions Based on Aitchison Geometry

The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison＇s ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space.     

Equilibrium States in the Quadruple–Kerr Solution

The extended quadruple–Kerr metric is used to consider equilibrium states of four collinear Kerr particles. We explain our previous failure to solve numerically the full set of the balance equations, and we derive a self–consistent system of the axis conditions leading to the equilibrium of all four constituents which can be black holes or hyperextreme objects. The equilibrium configurations obtained in this paper exhibit similar features with those occurring in the systems of two Kerr particles, for instance, the balance of four Kerr black holes with positive masses does not seem possible. Equilibrium states of two identical compound Kerr objects are also discussed.     

Design of a widely tunable laser with a chirped ladder filter

We theoretically investigated a digitally tunable laser with a chirped ladder filter and a ring resonator to obtain a wide wavelength tuning range covering the whole C- or L- band. The clear relation between the tuning range and laser structure, especially the ladder filter, is described analytically. The introduction of a chirped structure into a ladder filter is effective in achieving both wide tunability and a stable lasing mode. A numerical simulation based on multimode rate equations shows that a tuning range of over 40 nm and a mode suppression ratio over 40 dB can be achieved by introducing a chirped ladder filter.     

Maximum overlap symmetry molecular orbital model

This paper provides a brief and systematic presentation of the basic principle and method of the maximum overlap symmetry molecular orbital (MOSMO ) model and its application to simplification of molecular orbital calculation and to calculation of molecular structures and properties, together with some new results about the MOSMO calculation and new insights concerning the further extension of the principle and method. It has been shown that the theoretical method of the MOSMO model is very simple, reliable, and useful and can be employed to study the structure–property relation in even very large molecular systems. The numerical results obtained from the MOSMO calculation on various semiempirical molecular orbital approximation levels show that when the same parametrization, such as one of those employed in EHMO , CNDO /2, and HMO methods, is adopted, the MOSMOS are very close to the canonical molecular orbitals obtained from the customary LCAO method and the MOSMO calculation requires less computing time than does the LCAO method. The MOSMO calculation can be used for rapidly obtaining reasonably good molecular geometries, vibrational frequencies, and other properties of molecules by employing a simple improved semiempirical parametrization. Equilibrium geometries, vibrational frequencies, and other results are in good agreement with the experimental data and the results obtained from ab initio molecular orbital calculation. The basic calculational procedure of the MOSMO model can be extended further and has been employed to give some new results, to propose some new theoretical schemes and principles, and to introduce some new interesting theoretical problems that deserve to be studied further.     

Effect of synthesis method and buffer composition on the LCST of a smart copolymer of N‐isopropylacrylamide and acrylic acid

Responsive polymers have been the focus of many studies during the past decade because of their ability to change according to environmental stimuli. In this paper, we report on the development of a method to synthesize a pH/temperature‐sensitive linear copolymer, poly(N‐isopropylacrylamide‐ co‐acrylic acid)(poly(NIPAAm‐co‐AAc)), with a molecular weight of about 10⁶–10⁵ Da in water using azobisisobutyronitrile (AIBN) as the initiator. The effects of the following on the lower critical solution temperature (LCST) of the copolymer and homopolymer of NIPAAm were investigated: the type of buffer salts and pH changes of test solutions, molecular weight and concentration of homopolymer/copolymer solutions, and AAc monomer molar feed ratio (mol%). The effects of different synthesis methods on the molecular weight and on the AAc content were also evaluated. The mechanism of action in environments with different pH values is discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

Assessment of Noise Exposure of Sawmill Workers in Southwest,Nigeria

Economic wood processing employs the use of industrial machines for cutting, shaping, milling, and sawing timber, thereby leading to the generation of high levels of noise. Published data from empirical studies have categorized noise as an environmental hazard of global significance. Furthermore, noise exposure limits for different industries and all the industrial machines available has not been formally established as it presently exists in developed nations around the world. Therefore, this study assessed the daily exposure of sawmills workers to noise in Southwestern Nigeria. Reconnaissance surveys were first carried out in Osun, Oyo, Ondo, Ekiti, Lagos, and Ogun States to select sawmills that were fully operational and fit for the study. Two fully functional sawmills in two cities of each State were eventually selected for data collection, making a total of 24 sawmills, while the Circular Machines (CM), Planer Machines (PM), and Band-saw Machines (BM) were the machines in each sawmill considered. Two machines each of CM, PM, and BM were considered in each sawmill, making a total of forty-eight (48) machines each of CM, PM, and BM. Sound data were collected between 7 am and 7 pm each day for six days (between Monday and Saturday) using Extech 407732 sound level meter and all stabilized measurements were taken three times at different intervals. The data collected were in three different periods: Machine No-work Period (NP_m), Machine Idle Period (IP_m), and Machine Working Period (WP_m). A two–way Analysis of Variance (ANOVA) was carried out at P < 0.05 to determine whether there is a significant difference in the sound level average before and after the break, for both the idle and working periods of the three machines considered. This was also done to determine whether there is a significant difference between the sound level average of the results collected during idle and working periods of the three machines. Noise Pollution Levels (L_np) ranged from 83.20 dB (PM) to 107.65 (BM) and 93.42 (CM and PM) – 116.00 (BM) respectively, while IP_m also gave the least noise pollution level of 95.79 dB and WP_m gave the highest level of 102.88 dB. The results revealed that all the machines’ L_np values in the working period are more than the 90 dB acceptable limit the recommendation value of 90 dB while 89.6% of CMs, 75% of PMs, and 89.6% of BM had their L_np above 90 dB in the idle period respectively. The minimum and the maximum noise dose levels for IP_m, WP_m and overall are 0.09 (BM) and 2.37 (CM), 0.50 (CM), and 4.77 (PM) and 0.69 (BM) and 6.64 (PM) respectively. The study found out that the fundamental contributing factors to the high noise levels in sawmills are poor machine maintenance, use of old and obsolete machines, poor housekeeping strategy, limited space, workers’ negligence, lack of PPE, and lack of occupational safety training. The study recommends that proper workplace practices such as use of personal protective equipment, new and modern machines, training, and occupational safety programmes be implemented in the considered sawmills.     

On the use of surfaces of section in the N-body ring problem

In the N-body ring problem, we investigate the motion of a massless body interacting with N bodies of equal masses at the vertices of a regular polygon that rotates around a central mass. In this paper, we analyze the use of different surfaces of section in the numerical exploration of the escape in the N-body ring problem in order to get some conclusions about the geometry of the basins of escape in the corresponding configuration spaces.     

How Constant Momentum Acceleration Decouples Energy and Space Focusing in Distance–of–Flight and Time–of–Flight Mass Spectrometries

Resolution in time–of–flight mass spectrometry (TOFMS) is ordinarily limited by the initial energy and space distributions within an instrument’s acceleration region and by the length of the field–free flight zone. With gaseous ion sources, these distributions lead to systematic flight–time errors that cannot be simultaneously corrected with conventional static–field ion–focusing devices (i.e., an ion mirror). It is known that initial energy and space distributions produce non–linearly correlated errors in both ion velocity and exit time from the acceleration region. Here we reinvestigate an old acceleration technique, constant–momentum acceleration (CMA), to decouple the effects of initial energy and space distributions. In CMA, only initial ion energies (and not their positions) affect the velocity ions gain. Therefore, with CMA, the spatial distribution within the acceleration region can be manipulated without creating ion–velocity error. The velocity differences caused by a spread in initial ion energy can be corrected with an ion mirror. We discuss here the use of CMA and independent focusing of energy and space distributions for both distance–of–flight mass spectrometry (DOFMS) and TOFMS. Performance characteristics of our CMA–DOFMS and CMA–TOFMS instrument, fitted with a glow–discharge ionization source, are described. In CMA–DOFMS, resolving powers (FWHM) of greater than 1000 are achieved for atomic ions with a flight length of 285 mm. In CMA–TOFMS, only ions over a narrow range of m/z values can be energy–focused; however, the technique offers improved resolution for these focused ions, with resolving powers of greater than 2000 for a separation distance of 350 mm.      

Singularity-free cosmological solutions with non-rotating perfect fluids

A conjecture stated by Raychaudhuri which claims that the only physical perfect fluid non-rotating non-singular cosmological models are comprised in the Ruiz–Senovilla and Fernández–Jambrina families is shown to be incorrect. An explicit counterexample is provided and the failure of the argument leading to the result is explicitly pointed out.