Spherical means with centers on a hyperplane in even dimensions

Given a real-valued function on R-n we study the problem of recovering the function from its spherical means over spheres centered on a hyperplane. An old paper of Bukhgeim and Kardakov derived an inversion formula for the odd n case with great simplicity and economy. We apply their method to derive an inversion formula for the even n case. A feature of our inversion formula, for the even n case, is that it does not require the Fourier transform of the mean values or the use of the Hilbert transform, unlike the previously known inversion formulas for the even n case. Along the way, we extend the isometry identity of Bukhgeim and Kardakov for odd n, for solutions of the wave equation, to the even n case.

Fractional damping: Stochastic origin and finite approximations

Fractional-order derivatives appear in various engineering applications including models for viscoelastic damping. Damping behavior of materials, if modeled using linear, constant coefficient differential equations, cannot include the long memory that fractional-order derivatives require. However, sufficiently great rnicrostructural disorder can lead, statistically, to macroscopic behavior well approximated by fractional order derivatives. The idea has appeared in the physics literature, but may interest an engineering audience. This idea in turn leads to an infinite-dimensional system without memory; a routine Galerkin projection on that infinite-dimensional system leads to a finite dimensional system of ordinary differential equations (ODEs) (integer order) that matches the fractional-order behavior over user-specifiable, but finite, frequency ranges. For extreme frequencies (small or large), the approximation is poor. This is unavoidable, and users interested in such extremes or in the fundamental aspects of true fractional derivatives must take note of it. However, mismatch in extreme frequencies outside the range of interest for a particular model of a real material may have little engineering impact.

New insights from a fixed-point analysis of single cell IEEE 802.11 WLANs

We study a fixed-point formalization of the well-known analysis of Bianchi. We provide a significant simplification and generalization of the analysis. In this more general framework, the fixed-point solution and performance measures resulting from it are studied. Uniqueness of the fixed point is established. Simple and general throughput formulas are provided. It is shown that the throughput of any flow will be bounded by the one with the smallest transmission rate. The aggregate throughput is bounded by the reciprocal of the harmonic mean of the transmission rates. In an asymptotic regime with a large number of nodes, explicit formulas for the collision probability, the aggregate attempt rate, and the aggregate throughput are provided. The results from the analysis are compared with ns2 simulations and also with an exact Markov model of the backoff process. It is shown how the saturated network analysis can be used to obtain TCP transfer throughputs in some cases.

Studies on some metal monothiobenzoates

Monothiobenzoate (MTB) (Chemical Equation Presented) complexes with the molecular formulas Cr(MTB)3, [Ni(MTB)2]n, [Zn(MTB)2]n, [Cd(MTB)2]n, [Hg(MTB)2]n, [Cu(MTB)]n, and [Ag(MTB)]n have been prepared and studied. All the complexes are nonionic in acetonitrile. Only the chromium complex is soluble in nitrobenzene and found to be monomeric cryoscopically. The thiobenzoate ligand appears to be asymmetrically chelated in Cr(III) and Cd(II) complexes, with stronger oxygen and sulfur coordination, respectively, while practically symmetrically coordinated in Ni(II) and Zn(II) complexes. These four complexes are assigned distorted octahedral structures around the metal ion. The coordination in Hg(II), Cu(I), and Ag(I) complexes is mainly through sulfur indicating the monodentate nature of the thiobenzoate ligand in these complexes. The coordination of monothiobenzoate ion in the complexes has been rationalized in terms of "hard" and "soft" acid-base concept.

Refinement of the thermodynamic properties of ruthenium dioxide and osmium dioxide

The standard Gibbs energies of formation of RuO2 and OsO2 at high temperature have been determined with high precision, using a novel apparatus that incorporates a buffer electrode between the reference and working electrodes, The buffer electrode absorbs the electrochemical flux of oxygen through the solid electrolyte from the electrode with higher oxygen chemical potential to the electrode with lower oxygen potential, The buffer electrode prevents polarization of the measuring electrode and ensures accurate data, The standard Gibbs energies of formation (Delta(f)G degrees) of RuO2, in the temperature range of 900-1500 K, and OsO2, in the range of 900-1200 K, can be represented by the equations Delta(f)G degrees(RuO2)(J/mol) = -324 720 + 354.21T - 23.490T In T Delta(f)G degrees(OsO2)(J/mol) = -304 740 + 318.80T - 18.444T In T where the temperature T is given in Kelvin and the deviation of the measurement is +/- 80 J/mol, The high-temperature heat ;capacities of RuO2 and OsO2 are measured using differential scanning calorimetry. The information for both the low- and high-temperature heat rapacity of RuO2 is coupled with the Delta(f)G degrees data obtained in this study to evaluate the standard enthalpy of formation of RuO2 at 298.15 K (Delta(f)H degrees(298.15K)). The low-temperature heat capacity of OsO2 has not been measured: therefore, the standard enthalpy and entropy of formation of OsO2 at 298.15 K (Delta(f)H degrees(298.15K) and S degrees(298.15K), respectively) are derived simultaneously through an optimization procedure from the high-temperature heat capacity and the Gibbs energy of formation. Both Delta fH degrees(298.15K) and S degrees(298.15K) are treated as variables in the optimization routine, For RuO2, the standard enthalpy of formation at 298.15 K is Delta fH degrees(298.15K) (RuO2) -313.52 +/- 0.08 kJ/mol, and that for OsO2 is Delta(f)H degrees(298.15K) (OSO2) = -295.96 +/- 0.08 kJ/mol. The standard entropy of OsO2 at 298.15 K that has been obtained from the optimization is given as S degrees(298.15K) (OsO2) = 49.8 +/- 0.2 J (mol K)(-1).

Prediction of inplane damping from deterministic and stochastic models

This paper reviews computational reliability, computer algebra, stochastic stability and rotating frame turbulence (RFT) in the context of predicting the blade inplane mode stability, a mode which is at best weakly damped. Computational reliability can be built into routine Floquet analysis involving trim analysis and eigenanalysis, and a highly portable special purpose processor restricted to rotorcraft dynamics analysis is found to be more economical than a multipurpose processor. While the RFT effects are dominant in turbulence modeling, the finding that turbulence stabilizes the inplane mode is based on the assumption that turbulence is white noise.

Invariant-preserving Petri net reduction and conditions for invariant-existence

The use of invariants is an important tool for analysis of distributed and concurrent systems modeled by Petri nets. For a large practical system, the computation of desired invariants by the existing techniques is a time-consuming task. This paper proposes a theoretical foundation for simplified computation of desired invariants. We provide invariant-preserving Petri net reduction rules followed by the conditions for the existence of invariants in various well-structured nets. If an invariant exists, it can be found directly from the net structure using the formulas derived, or by applying the existing techniques on the reduced net.

Lectin Microarrays for Glycomic Analysis

Glycomics is the study of comprehensive structural elucidation and characterization of all glycoforms found in nature and their dynamic spatiotemporal changes that are associated with biological processes. Glycocalyx of mammalian cells actively participate in cell-cell, cell-matrix, and cell-pathogen interactions, which impact embryogenesis, growth and development, homeostasis, infection and immunity, signaling, malignancy, and metabolic disorders. Relative to genomics and proteomics, glycomics is just growing out of infancy with great potential in biomedicine for biomarker discovery, diagnosis, and treatment. However, the immense diversity and complexity of glycan structures and their multiple modes of interactions with proteins pose great challenges for development of analytical tools for delineating structure function relationships and understanding glycocode. Several tools are being developed for glycan profiling based on chromatography,m mass spectrometry, glycan microarrays, and glyco-informatics. Lectins, which have long been used in glyco-immunology, printed on a microarray provide a versatile platform for rapid high throughput analysis of glycoforms of biological samples. Herein, we summarize technological advances in lectin microarrays and critically review their impact on glycomics analysis. Challenges remain in terms of expansion to include nonplant derived lectins, standardization for routine clinical use, development of recombinant lectins, and exploration of plant kingdom for discovery of novel lectins.

Radical cyclization strategies to terpenoids; syntheses of (±)-β-cuparenone, (±)-laurene and epilaurenes

Radical cyclization of the bromide Image , obtained in 5 steps from the ketone Image , furnished exclusively Image Image 6-endo trig cyclization with out any observable amount of 5-exo trig product Image . 5-Exo dig radical cyclizatlon of the bromo acetate Image , prepared from Image Image the aldehyde Image , followed by routine transformations furnished the cyclopentenone Image , an immediate precursor to β-cuparenone (Image ). Similarly, total synthesis of laurenes Image and Image was achieved Image the 5-exo dig radical cyclization of the xanthate Image , obtained from the aldehyde Image .Syntheses to title compounds based on 5-exo-dig radical cyclisation, along with two unsuccessful approaches to cuparene, are described.

Stress and strength analysis of pin joints in laminated anisotropic plates

Mechanical joints in composites can be tailored to achieve improved performance and better life by appropriately selecting the laminate parameters. In order to gain the best advantage of this possibility of tailoring the laminate, it is necessary to understand the influence of laminate parameters on the behaviour of joints in composites. Most of the earlier studies in this direction were based on simplified assumptions regarding load transfer at the pin-plate interface and such studies were only carried out on orthotropic and quasi-isotropic laminates. In the present study, a more rigorous analysis is carried out to study pin joints in laminates with anisotropic properties. Two types of laminates with (0/ + ?4/90)s and (0/ ± ?2/90)s layups made out of graphite epoxy T300/5208 material system are considered. The analysis mainly concentrates on clearance fit in which the pin is of smaller diameter compared to the hole. The main aspect of the analysis of pin joints is the changing contact between the pin and the plate with increasing load levels. The analysis is carried out by an iterative finite element technique and a computationally efficient routine is developed for this purpose. Numerical studies indicate that the location and magnitude of the peak stresses along the hole boundary are functions of fibre angle and the overall anisotropic properties. It is also shown that the conventional assumption of cosine distribution for the contact pressure between pin and the plate in the analysis lead to underestimation of bearing failure load and overestimation of shear and tensile failure loads in typical (0/905)s cross-ply laminates.

Three Dimensional Line-Clipping by Systematic Enumeration

Three dimensional clipping is a critical component of the 3D graphics pipeline. A new 3D clipping algorithm is presented in this paper. An efficient 2D clipping routine reported earlier has been used as a submodule. This algorithm uses a new classification scheme for lines of all possible orientations with respect to a rectangular parallelopiped view volume. The performance of this algorithm has been evaluated using exact arithmetic operation counts. It is shown that our algorithm requires less arithmetic operations than the Cyrus-Beck 3D clipping algorithm in all cases. It is also shown that for lines that intersect the clipping volume, our algorithm performs better than the Liang-Barsky 3D clipping algorithm.

Generalized State Parameter for Partly Saturated Soils

Studies on compressibility and shear strength aspects are the concern of many investigators concerned with partly saturated soils. In soil engineering connected with partly saturated soils, there are no approaches connecting soil states and stress conditions. The present investigation is essentially a step in this direction. A generalized state parameter, identified with regard to material states is shown to be related to the compressibility and shear strength. The involved parameters are simple and normally determined in routine investigations. The advantage of this approach is that changes in soil states due to external stress conditions and the associated changes in strength can be examined particularly when different types of soils are involved.

Affine Hall-Littlewood Functions for A(1)((1)) And Some Constant Term Identities of Cherednik-Macdonald-Mehta Type

We study t-analogs of string functions for integrable highest weight representations of the affine Kac-Moody algebra A(1)((1)). We obtain closed form formulas for certain t-string functions of levels 2 and 4. As corollaries, we obtain explicit identities for the corresponding affine Hall-Littlewood functions, as well as higher level generalizations of Cherednik's Macdonald and Macdonald-Mehta constant term identities.

Can one electrochemically measure the statistical morphology of a rough electrode

We have developed a theory for an electrochemical way of measuring the statistical properties of a nonfractally rough electrode. We obtained the expression for the current transient on a rough electrode which shows three times regions: short and long time limits and the transition region between them. The expressions for these time ranges are exploited to extract morphological information about the surface roughness. In the short and long time regimes, we extract information regarding various morphological features like the roughness factor, average roughness, curvature, correlation length, dimensionality of roughness, and polynomial approximation for the correlation function. The formulas for the surface structure factors (the measure of surface roughness) of rough surfaces in terms of measured reversible and diffusion-limited current transients are also obtained. Finally, we explore the feasibility of making such measurements.

Frontier Based Multiple Goal Search in Unknown Environments

We present a frontier based algorithm for searching multiple goals in a fully unknown environment, with only information about the regions where the goals are most likely to be located. Our algorithm chooses an ``active goal'' from the ``active goal list'' generated by running a Traveling Salesman Problem (Tsp) routine with the given centroid locations of the goal regions. We use the concept of ``goal switching'' which helps not only in reaching more number of goals in given time, but also prevents unnecessary search around the goals that are not accessible (surrounded by walls). The simulation study shows that our algorithm outperforms Multi-Heuristic LRTA* (MELRTA*) which is a significant representative of multiple goal search approaches in an unknown environment, especially in environments with wall like obstacles.