Palestinian Conference on Modern Trends in Mathematics and Physics II

Let R be a commutative ring with 1 6= 0 and Nil(R) be its set of nilpotent elements. Recall that a prime ideal of R is called a divided prime if P ½ (x) for every x 2 RnP. The class of rings: H = fR j R is a commutative ring and Nil(R) is a divided prime ideal of Rg has been studied extensively by the speaker(i.e. Badawi). Observe that if R is an integral domain, then R 2 H. Hence H is a much larger class than the class of integral domains. If R 2 H, then R is called a Á-ring.
I wrote the ¯rst paper on Á-rings in 1999 :"Á-pseudo-valuation rings," appeared in Advances in Commutative Ring Theory, 101-110, Lecture Notes Pure Appl. Math. 205, Marcel Dekker, New York/Basel, 1999.

Production and regulation of erythrocytes (red blood cells) is performed through complex processes. Cells are produced in the bone marrow (and the spleen, in mice), where hematopoietic stem cells, that have abilities of self-renewal and differentiation in all blood cell types, allow the appearance of erythroid cells. Throughout successive diviffsions, erythroid progenitors (immature red cells) acquire maturity (via cell markers) to ultimately become mature red blood cells (erythrocytes) that enter the bloodstream in order to carry oxygen to organs and tissues.
This continuous production of erythroid cells is permanently controlled in order to adapt very quickly to changes in or needs of the organism. One of the main feedback controls, discovered in the early 1990's by Koury and Bondurant [3] deals with cell death. Erythroid progenitors die by apoptosis, a programmed cell death (contrary to necrosis). Koury and Bondurant showed that, during an anemia (lack of red blood cells), a growth factor named erythropoietin (Epo) was released by the kidneys and inhibited progenitor apoptosis, allowing a fast production of numerous erythrocytes to get a correct level of red blood cells in blood.
Others controls occur at early stages of erythropoiesis, for instance differentiation of hematopoietic stem cells in cells committed to the red blood cell lineage is partly controlled by Epo. In the presence of Epo, hematopoietic stem cells will preferentially differentiate in red blood cells rather than in white blood cells or platelets.

In this study the interaction of steroid hormones (progesterone and its parent compound cholesterol) with human serum albumin at physiological pH have been studied using UV-VIS spectrophotometer, fluorescence spectrophotometer, and FT-IR spectroscopy. The results showed that UV absorption intensity spectra were increased with the increase of progesterone or cholesterol molar ratios in fixed amount of HSA. From UV spectra the binding constants were obtained and equals (6.354×102M-1)for progesterone and (0.2641×104M-1) for cholesterol. Beside that the results that have been obtained from analysis of fluorescence spectra indicated that progesterone and cholesterol have an ability to quench the intrinsic fluorescence of HSA through a static quenching procedure. The values of Stern-Volmer constant were determined to be (6.26×102 L mol-1) for progesterone- HSA complexes and (6.21×102 L mol-1) for cholesterol- HSA complexes. Also the quenching rate constant values obtained were (6.2×1010 L mol-1s-1) for progesterone and (6.21 × 1010 Lmol-1s-1) for cholesterol.
The binding constant from fluorescence spectrum for progesterone- HSA complexes was found to be (6.56×102 M-1). And for cholesterol- HSA complexes was found to be (0.214 × 104 M-1). It was obviously noted that the obtained values agrees well with the values obtained using UV-VIS spectrophotometer. And that cholesterol binding constant is larger than progesterone binding constant, this refer to the structure of the two compounds which is consistent with that have been reported. FT-IR spectroscopy with Fourier self-deconvolution and second derivative, as well as curve fitting procedures were used in the analysis of amide I, amide II, and amide III regions of HSA to determine protein secondary structure and hormone binding mechanism. It was observed that the intensity of absorption bands decreased as progesterone or cholesterol molar ratios increased. Also all peak positions of the three amide regions were assigned at different progesterone or cholesterol ratios. In addition FT-IR spectra evidence showed that HSA secondary structure has been changed as progesterone or cholesterol molar ratios increased, which was observed in the reduction of α-helices absorption band relative to β-sheets absorption band. The variation in the intensity is related indirectly to the formation of H-bonding in the complex molecules, which accorded for the different intrinsic propensities of α-helix and β-sheets.

The properties of the wave equation are studied in the case of energy-dependent potentials for discreet states. The non-linearity induced by the energy-dependence requires modifications of the standard rules of quantum mechanics. They are briefly recalled. We consider various radial shapes in the D = 3 dimensional space, assuming spherical symmetry and a linear energy dependence. This last is chosen because it produces a coherent theory.
We present the effects of the energy dependence on the spectra of one-body and many-body systems. The most spectacular result is the saturation of the spectrum in the case of confining potentials : as the quantum number increase, the eigenvalues reach an upper limit. We deal with the question of the equivalent local potential. We discuss the role of the energy-dependence in critical situations, and show, for instance, that is regularized the -1/r2 potential.

In the quest for new materials not surprising alloying has been an age old recipe as depicted by the shiny colors of a goblet from the 4th century supposedly signifying the unique optical properties of bimetallic (Ag-Au) nanoparticles. Boom in the modern era of systematic investigations of the properties of materials at the nanoscale came with the finding in 1997 by Haruta of enhanced reactivity of Au nanoparticles. Striking catalytic, electronic, magnetic, vibrational, optical and mechanical properties of nanoparticles have since been reported. Bimetallic nanoparticles are even more intriguing as composition is yet another switch that may control its novel characteristics which are expected to be different those of the bulk alloy (for examples metals that do not mix in the bulk material are found to be miscible at the nanoscale). In this talk after a brief review, I will consider two types of nanoalloys: bimetallic nanoparticles and islets of one metal on facets of another. I will examine competing factors that may conspire to produce stable configurations in each case and track how the vibrational, chemical and electronic structural properties of these nanoalloys vary with size, composition, and local environment. In the case of the Ag-Cu nanoparticles, the focus will be on understanding the factors that control the relative stability of a set of 34-atom particles of varying composition and how vibrational properties may serve as signatures of alloy composition [1,2]. In the case of Pt islets on Ru nanoparticles, the focus will be on changes in electronic structural properties induced by allowing that make this nanoalloy very attractive as a fuel cell anode catalyst [3].

This study reports the association of noise pollution level with blood pressure (systolic and diastolic) and heart pulse rate in schools’ children. The test sample schools consist of six different schools chosen randomly in Jenin city. The measured sound pressure levels (SPL) in all tested schools were found to be above the standard international acceptable levels. Strong positive correlation (person correlation coefficient) was found between sound pressure levels in the sample schools from one side and blood pressures (R=0.285 for both systolic and diastolic) and heart pulse rate (R=0.273) from the other side. The average change rate of systolic and dyastolic blood pressures were found to be about 5 mm-Hg and 2.7 mm-Hg for every 75dB/hr change in SPL values, respectively. Also, the average rate of change of heart pulse rate was found to be about 5beats/min which reflects the strong correlation between changes of systolic blood pressure and heart pulse rate.

The standard contact structure of has a vector-field defining a Hopf fibration in its kernel. Legendre transform w.r.t can be performed. Symmetric Hamiltonian problems are thereby transformed into their Lagrangian counterparts. It was believed that the existence of such a was special to this framework. This belief turns out to be wrong. V. Martino has produced a vector-field in the kernel of the first contact form by J.Gonzalo and F.Varela such that is also a contact form with the same orientation than α. This provides a new textbook example in Contact Form Geometry. We will describe in our talk the first contact form of J.Gonzalo and F.Varela and the vector-field in its kernel by V.Martino; we will study the related dynamics and the related Reeb vector-fields periodic orbit problems at the light of the homology for contact forms/structures that we have defined in our work.

The Matrix representation of the molecular graph is studied and re-written in new forms. We study and present the eigenvalues and eigenvectors of the star graph. In order to that we state and prove two theorems that finding the eigenvalues and eigenvectors of the star graphs. We relate these eigenvalues and eigenvectors with the physico-chemical prosperities of the molecule under consideration. Finally few examples are given.

We will investigate both autonomous and non autonomous periodic competition models. Our main focus is to study invariant stable, unstable, and center manifolds using analytical and numerical methods. In addition, bifurcation analysis will be presented. Finally some open problems and conjectures will be discussed.

In 1960 Overhauser [1] suggested that the ground state of nuclear matter may not be described by plane wave orbitals corresponding to a uniform density fluid phase but rather by orbitals that produce a periodically varying density. Such Overhauser orbitals were shown [2] to give an energy lower than that obtained from plane waves, but only at low densities. Such periodic densities correspond to α particle-like clusters arranged on a lattice and thus correspond to a solid phase. These results were subsequently extended to finite temperature [3] and a triple point of nuclear matter was found at a temperature of about 1.1 MeV. Recent experimental analyses of moderate-temperature nuclear gases produced in heavy ion reactions reveal a large degree of α particle clustering at low densities [4]. The thermodynamic properties and equation of state of low density nuclear matter, including cluster formation, will be examined.

The Aharonov-Bohm effect, first described in 1959, is among the most spectacular effects of quantum mechanics, emphasizing the role the electromagnetic potentials – and not the electromagnetic fields – play for the wave-like motion of quantum particles. Considering a ringlike geometry in a constant perpendicular magnetic field, a direct consequence is that all properties of a charged system are periodic functions of the magnetic flux, Φ, the flux periodicity given by the fundamental flux quantum, Φ0 = h/e. This result is based on the particular combination, p + eA, which appears in the Hamiltonian of the system, where p is the momentum, and A the vector potential; here we consider electronic systems, and the charge of an electron is –e.
In equilibrium, the system’s properties can be calculated from the partition function, which involves a trace over all states of the systems: hence in the classical limit any flux dependence disappears (Bohr-van-Leeuwen-Theorem), and the persistent current, I(Φ) = –∂F(Φ)/∂Φ, vanishes; F(Φ) denotes the thermodynamic potential. Thus very small systems and very low temperatures are required for a finite (non-zero) I(Φ) to exist.
In fact “normal” persistent currents, of the order of a few nA, have been seen in several experiments, for temperatures below 1 K [1–4]. In contrast to the experiments [1–3] which used a SQUID technique in order to detect the magnetic moment induced by the current, the most recent study [4] employed a nano-electromechanical technique: the rings were placed on a cantilever, whose oscillation frequency can be measured with extremely high accuracy. The perimeter of the studied rings varied between 0.6 and 1.6 μm.
Assuming time reversal invariance, the Fourier expansion of the persistent current is given by I(Φ) = I1 sin (2πΦ/Φ0) + I2 sin (4πΦ/Φ0) + … .
Because of the disorder always present in small rings, due to the fabrication process, the amplitudes I1 and I2 are random quantities. For example, I1 fluctuates from ring to ring; in particular, it changes its sign, hence the average is expected (and was found) to be zero. The size of ‹(I1)2›1/2, on the other hand, has been debated for many years; the theoretical prediction ‹(I1)2›1/2 ≈ Ec/Φ0 [5] was now convincingly confirmed [4]; here Ec = hD/L2 is called Thouless energy, D is the diffusion constant, and L the perimeter of the ring. Concerning the second harmonic, I2, it was pointed out rather early [6] that the effective electron-electron interaction gives an important contribution, which nevertheless is too small compared to the experimental result [1]. A recent paper discusses the question whether a small amount of paramagnetic impurities can resolve this discrepancy [7]. For an introduction into persistent currents, see [8].

We measure the transmission of O6+ ions with a higher energy of 60 keV (in turn a higher value of Ep/q) through capillaries in an uncoated Al2O3 membrane, and obtain agreements with previously reported results in general angular distribution of the transmitted ions and the transmission profile width variation with capillary tilt angle.
The transmission fractions as a function of the tilt angle can be fitted to the semi-empirical Gaussian-like function well. Due to using uncoated capillary membrane, our ψc is larger than that using gold-coated one, in spite of our larger value of Ep/q, which suggests a larger equilibrium charge Q∞ in our experiment.

The effect of infrared laser of wavelength (λ = 1064nm), pulse energy of 40 mJ/pulse at a repetition rate of 10 Hz, on the activation energy of CR-39 solid state nuclear track detector has been investigated. Fifteen detectors were divided into three sets of equal numbers. The first set (post-exposed) was first exposed to alpha radiation with close contact to the 241Am source and then treated in air with laser at energy intensity 8 J/cm2. For the second set (pre-exposed), the process was reversed (laser + alpha) under the same conditions. The third set (unexposed to laser beam) was irradiated in close contact with the same alpha source (241Am). The activation energy of track etch (EV) for post-exposed, pre-exposed and unexposed was found equal to 0.887, 0.914 and 0.671 eV, respectively. The respective activation energies of bulk etch (EB) for post-exposed, pre-exposed and unexposed was found equal to 0.984, 0.912 and 0.926 eV.
From these measurements, it is concluded that the laser exposure led to the hardening of the material of the detector as evidenced from the values of activation energies for both bulk and track etch.

The main object of the present paper is to derive a number of key formulas for the fractional integration of the multivariable H-function (which is defined by a multiple contour integral of Mellin-Barnes type). Each of the general Eulerian integral formulas (obtained in this paper) are shown to yield interesting new results for various families of generalized hypergeometric functions of several variables. Some of these applications of the key formulas would provide potentially useful generalizations of known results in the theory of fractional calculus.

The passage of light through apertures much smaller than the wavelength of the light has proved to be a surprisingly subtle phenomenon. This talk describes how modern developments in nanofabrication, coherent light sources and numerical vector field simulations have led to the upending of early predictions from scalar diffraction theory and classical electrodynamics. Optical response of real materials to incident coherent radiation at petahertz frequencies leads to unexpected consequences for transmission (and extinction) of light through sub wavelength aperture arrays.

The interaction between pentobarbital and human serum albumin has been investigated. The basic binding interaction was studied by UV-absorption and fluorescence spectroscopy. From spectral analysis pentobarbital showed a strong ability to quench the intrinsic fluorescence of HSA through a static quenching procedure. The binding constant (k) is estimated at 1.812 * 104 M-1 at 293 K. FT-IR spectroscopy with Fourier self deconvolution technique was used to determine the protein secondary structure and drug binding mechanisms. The observed spectral changes of HSA–pentobarbital complex indicate a larger intensity decrease in the absorption band of α-helix relative to that of β-sheets. This variation in intensity is related indirectly to the formation of H-bonding in the complex molecules, which accounts for the different intrinsic propensities of α-helix and β-sheets.

Palestine has limited natural resources. Any future development should therefore be based on advanced technology. Such ambitious outlook dictates that Palestine heavily invests in quality teaching and researching in such areas. Materials research is one building block for building advanced technology. The philosophy is simple: we need to develop a technology which intensively demands know-how rather than resources. In short Palestine should develop a technology based on creativity and invention, starting with advanced materials and their applications.
Advanced materials include a wide range of areas such as nanotechnology, thin films, nanodevices, conductive polymers and others. Applications of advanced materials span a number of areas such as: Energy storage devices (super batteries supercapacitors, fuel cells), clean energy (photovoltaics PV, photoelectrochemistry PEC) biotechnology (drug delivery, cancer treatment), superconductivity & superconducting magnets (MRI, super-trains) and other applications (LEDs, electrochromics).

Semiconductors (AC) are a very important area of advanced materials. Almost all contemporary technologies rely on SC systems such as p-n junctions (transistors, diodes, PV, PEC, refrigeration…).
In this plenary, we wish to give one specific example on where Palestinian scientists can target an area of advanced material research and can contribute effectively despite limited resources. Semiconductor research activity has been established in the laboratories of An-Najah N. University in the mid 1990s. The activity started with modification of mono-crystalline n-Si and n-GaAs semiconductor surfaces for the purpose of controlling band edge positions. This was for the purpose of tailoring band edge positions to catalyze water splitting (into hydrogen and oxygen) by solar light. The objectives were successfully achieved by graduate students at ANU. To simultaneously achieve stability and efficiency of the SC electrode, other techniques were developed here. Monocrystallyne n-GaAs electrodes were enhanced in stability and efficiency using polymeric coatings with electroactroactive ions inside. However, the increasing cost of monocrystalline SC materials affected our objective. Our efforts were then diverted to synthetic thin film SC electrodes. Preparation of enhanced semiconducting materials, in the forms of thin films and nano-scale particles, have then been conducted for the purposes of light-to-electricity and water decontamination strategies, have been established.

Recently our students have been heavily engaged in preparing new classes of n-type semiconducting materials (CdS and CdSe) in the forms of thin films and nano-scale particles using Chemical Bath Deposition (CBD) and Electro-Chemical Deposition (ECD) techniques. Thin CdS and CdSe films were deposited onto FTO/glass systems and are currently being used for light-to-electricity conversion processes. Modification of thin films with different techniques shows promising potential in enhancing efficiency and stability. For the first time, ANU students were able to stabilize CBD-based CdSe films in PEC processes.

Examples of SC research progress at ANU will be highlighted in this presentation. Some technical results and discussions will be presented. This is to give examples to young Palestinian scientists on what they can achieve should they work in advanced materials research, directed towards solving societal problems. It is also intended to attract the attention of decision makers to put materials R&D as a high priority area in the near future.