Some Solutions for a Class of Singular Equations

In this paper we obtain all solutions which depend only on r for a class of partial differential equations of higher order with singular coefficients.     

A new efficient presentation for PSL(2,5) and the structure of the groups G(3,m,n)

G(3, m, n) is the group presented by . In this paper, we study the structure of G(3, m, n). We also give a new efficient presentation for the Projective Special Linear group PSL(2, 5) and in particular we prove that PSL(2, 5) is isomorphic to G(3, m, n) under certain conditions.     

The -theory of toric manifolds

Toric manifolds, a topological generalization of smooth projective toric varieties, are determined by an -dimensional simple convex polytope and a function from the set of codimension-one faces into the primitive vectors of an integer lattice. Their cohomology was determined by Davis and Januszkiewicz in 1991 and corresponds with the theorem of Danilov-Jurkiewicz in the toric variety case. Recently it has been shown by Buchstaber and Ray that they generate the complex cobordism ring. We use the Adams spectral sequence to compute the -theory of all toric manifolds and certain singular toric varieties.

     

A Dielectric Chirped Layered Mirror for Optical Telecommunication Wavelengths

We describe in this paper a design procedure for omnidirectional high reflectors with wide bandwidths for optical telecommunication bands. From the numerical results achieved by the transfer matrix method, it is found that a partial omnidirectional high-reflector covering the optical telecommunication wavelengths 1.3 and 1.55 μm is obtained for a partially deformed quarter-wave stack air/H(LH)¹⁵/glass by using the tellurium as a material of high refractive index (n _H = 4.6). The partially deformed stack is a periodic system deformed by a power law y = x ^1+k. Here y is the coordinates of the deformed object, x is the coordinates of the periodic stack and k is the coefficient defining the deformation degree. The study of this system leads to an omnidirectional high reflector band covering the optical telecommunication wavelengths 1.3 and 1.55 μm for k = 0.2.     

The effect of parasitic boron doping on P-type piezoresistors

Absolute piezoresistive pressure sensors often use direct wafer bonding of SOI with the etched bulk silicon to provide us with sensitive membranes and sealed cavities. The advantage of such a process is that we can easily obtain a thin, monocrystalline silicon membrane with controlled thickness and a vacuum sealed cavity. However, few works have been reported on the electrical quality of this N-type membrane and its influence on performance of the P-type gauges. The problem of parasitic Boron appearance at the Si/SiO₂ interface was only recently shown in BESOI wafers, but it becomes much more significant when creating the component at the bottom side of the device layer, like in the case of an absolute piezoresistive pressure sensor.     

Hydroxy and methoxy substituted N 1,N 4-diarylidene-S-methylthiosemicarbazone iron(III) and nickel(II) complexes

Template reactions of 2,4-dihydroxy-, 2,5-dihydroxy-, 2-hydroxy-3-methoxy- and 2-hydroxy-4-methoxy-benzaldehyde with methoxy- and hydroxy-substituted salicylaldehyde S-methylthiosemicarbazones in the presence of NiCl₂ and FeCl₃ resulted in the corresponding hydroxy- and methoxy-substituted N¹,N⁴-diarylidene-S-methylthiosemi-carbazone complexes. Characterization of the compounds, [Fe(L)Cl] and [Ni(L)], was accomplished by means of elemental analysis, conductivity and magnetic measurements, i.r. and ¹H-n.m.r. spectra. A systematic trend has been observed for the chemical shift values of the aromatic protons in the spectra of complexes.     

Reconstruction and crosstalk of protein-protein interaction networks of Wnt and Hedgehog signaling in Drosophila melanogaster

In the last few years, researchers have an intense interest in the evolutionarily conserved signaling pathways which have crucial roles during embryonic development. The most intriguing factor of this interest is that malfunctioning of these signaling pathways (Hedgehog, Notch, Wnt etc.) leads to several human diseases, especially to cancer. This study deals with the β-catenin dependent branch of Wnt signaling and the Hedgehog signaling pathways which offer potential targeting points for cancer drug development. The identification of all proteins functioning in these signaling networks is crucial for the efforts of preventing tumor formation. Here, through integration of protein-protein interaction data and Gene Ontology annotations, Wnt/β-catenin and Hedgehog signaling networks consisting of proteins that have statistically high probability of being biologically related to these signaling pathways were reconstructed in Drosophila melanogaster. Next, by the structural network analyses, the crucial components functioning in these pathways were identified. The proteins Arm, Frizzled receptors (Fz and Fz2), Arr, Apc, Axn, Ci and Ptc were detected as the key proteins in these networks. Futhermore, the hub protein Mer having tumor suppressor function may be proposed as a putative drug target for cancer and deserves further investigation via experimental methods. Finally, the crosstalk analysis between the reconstructed networks reveals that these two signaling networks crosstalk to each other.     

Two-dimensional quaternion wavelet transform

In this paper we introduce the continuous quaternion wavelet transform (CQWT). We express the admissibility condition in terms of the (right-sided) quaternion Fourier transform. We show that its fundamental properties, such as inner product, norm relation, and inversion formula, can be established whenever the quaternion wavelets satisfy a particular admissibility condition. We present several examples of the CQWT. As an application we derive a Heisenberg type uncertainty principle for these extended wavelets.     

Dynamic pricing and scheduling in a multi-class single-server queueing system

This paper investigates an optimal sequencing and dynamic pricing problem for a two-class queueing system. Using a Markov Decision Process based model, we obtain structural characterizations of optimal policies. In particular, it is shown that the optimal pricing policy depends on the entire queue length vector but some monotonicity results prevail as the composition of this vector changes. A numerical study finds that static pricing policies may have significant suboptimality but simple dynamic pricing policies perform well in most situations.     

A study of sloshing absorber geometry for structural control with SPH

A liquid sloshing absorber consists of a container, partially filled with liquid. The absorber is attached to the structure to be controlled, and relies on the structure's motion to excite the liquid. Consequently, a sloshing wave is produced at the liquid free-surface within the absorber, possessing energy dissipative qualities. The primary objective of this work is to numerically demonstrate the effect of a sloshing absorber's shape on its control performance. Smoothed Particle Hydrodynamics (SPH) is used to model fluid–structure interaction of the structure/sloshing absorber system in two dimensions. The structure to be controlled is a lightly damped single degree-of-freedom structure. The structure is subjected to a transient excitation and then allowed to respond dynamically, coming to rest either due to its own damping alone or with the added control of the sloshing absorber. It is identified that the control performance of the conventionally used rectangular container geometry can be improved by having inward-angled walls. This new arrangement is robust, and of significant advantage in situations when the external disturbance is of uncertain magnitude.