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A thin film made from polyvinyl chloride (PVC) and methyl yellow (MY) was developed for potential application as a dosimeter for gamma irradiation. The PVC-MY film dosimeter was prepared by a simple solvent-casting method of the homogeneous solution containing PVC and MY. To investigate the potential application of the PVC-MY film as a dosimeter, the film was exposed to gamma radiation at absorbed doses of 0–20 kGy with a dose rate of 3.1 kGy/hour. The optical properties of the PVC-MY film were observed using a UV-Vis spectrophotometer in the wavelength range of 550–300 nm. The absorption spectra of different PVC-MY films revealed that the PVC-MY film has a maximum absorption at 419 nm and 527 nm. The absorption of the PVC-MY film at 419 nm decreased gradually as gamma-irradiation doses increased, while the film absorption at 527 nm increased as gamma-irradiation doses increased. The change in the absorption behavior of the PVC-MY film was also manifested in the change of the film color, where increasing radiation doses changed the film's color from yellow to red. The gamma dose-response curves of the PVC- MY film had a high correlative coefficient when described by a logarithmic function. These results demonstrated that PVC-MY film might potentially be a gamma-irradiation dosimeter in the dose range of 0–20 kGy. [ABSTRACT FROM AUTHOR]

The article considers the multiplication of negative numbers, says about the ability to take out minus one and work with negative numbers as with positive ones, while counting orders of minus one. If «minus times minus will be plus» then when a negative number is raised to a power a positive number is obtained which is uncharacteristic for mathematics as for the structure of numbers. If «minus times minus will be minus» then computational errors occur. Alternating powers of negative numbers are the basis of alternating series, their conditional and absolute convergence. We can consider two sets of positive and negative numbers and say that if we work on an adjacent set of both positive and negative numbers then «minus times minus will be plus», and if we work only on the set of negative numbers then «minus times minus will be minus». Then when raising negative numbers to a power negative numbers will be obtained, as it should be. And when multiplying two negative numbers, a negative number will be obtained if we work on a set of negative numbers. Then we can plot exponential and logarithmic functions with negative bases. [ABSTRACT FROM AUTHOR]

The inverse function is one of the topics discussed in high school. This study aimed to determine learning obstacles to learning that students face when studying the inverse functions. This study is using the didactical design research that involved ten students who had completed this topic. Students' responses toward examinations and interviews are analyzed to determine how they solved the inverse functions problems. The findings indicated that students encountered learning obstacles classified as epistemological, ontogenic, and didactical obstacles. The first result is that students experienced obstacles to determine the domain of the inverse function. They were capable of determining the inverses of functions but not their domain. Another obstacle that students face is a lack of understanding of the exponential and logarithmic functions and difficulties in sketching their graphs, which results in students being unable to address the problem of the inverse functions. The last obstacle is students' limited knowledge of fundamental topics in solving inverse functions. [ABSTRACT FROM AUTHOR]

In this work, the Hermite polynomial Hn(x) is used as the kernel of a multidimensional definite integral expressed in terms of the Hurwitz-Lerch Zeta function. Fundamental constants are used to evaluate special instances. [ABSTRACT FROM AUTHOR]

The pandemic of covid-19 has led to the change of learning activities from offline class into online learning. This online learning can be effective if it is supported by learning media that are appropriate to the learning conditions. Therefore, this study aims to appeal to the effectiveness of using the Quizizz website in online learning of logarithmic function material at SMAN 2 Mataram. This research was an experimental study with a post-test-only control group design. In this study, the experimental class and control class were selected by using a random sampling technique. In the experimental class, online learning was carried out for the material on logarithmic functions assisted by the Quizizz website. The facilities for creating slides (lessons) and quizzes on Quizizz were used as online learning media in the Experiment class. The control class was given the same material but with different treatment, which was online learning without Quizizz. The same post-test questions were given to determine the conceptual mastery of the two classes regarding the logarithmic function material. The data were analyzed using a two-tailed t-test with a significance level of 5%. Based on the results of the post-test score, the experimental class average score was higher than the control class. Based on the two-tailed of t-test we found that t-count (2.853) was higher than t table (2.002), we can conclude that there is a significant difference between the average score of the two classes. Based on the results of data analysis, it can be concluded that online learning using Quizizz on logarithmic function material is effective in helping students master the concept. [ABSTRACT FROM AUTHOR]

In this article, the researchers tries to prove that alpha Laplace transform can be applied to fractional system. By defining, alpha difference operator, the researchers tries to prove, several properties of the inverse fractional difference operator, we define a fractional alpha Laplace transform, denoted by Lvα(h) and fractional extorial transform, denoted by Evα(h) on time(t). Several identities, involving fractional difference operators are obtained for raising and falling h-factorials and Laplace and extorial transforms of factorial, geometric and logarithmic functions are also presented. Examples with diagrams, verified and generated by MATLAB, are provided as illustrations for the results presented. [ABSTRACT FROM AUTHOR]

The relativistic formulation of abstract evolution equations is introduced. The corresponding logarithmic representation is shown to exist without assuming the invertible property of evolution operators. Consequently, by means of the logarithmic representation of operators, nonlinear and discrete properties are shown to be valid to the infinitesimal generators of relativistic abstract evolution equations. [ABSTRACT FROM AUTHOR]

As a new array technique, frequency diverse array (FDA) has been proposed to overcome the disadvantages of phased array. Conventional FDA cannot be used in detection directly, due to its range-angle coupling problem and periodicity in range. Although, FDA with logarithmic frequency offset (Log-FDA) breaks the periodicity by applying a nonuniform offset, Log-FDA has limited applications when it is used for target detection and positioning. In this paper, for far-field target detection, a logarithmic frequency increment-based FDA using weighting function is proposed as the transmit array, while a phased array is used as the receive array. The proposed system scans full angles and it requires no priori information for the range or angle of targets. Meanwhile, transmit beampattern with low side lobes can be obtained which reduces the influence of interference. Range-angle imaging of far-field targets by the proposed system is verified by simulation results [ABSTRACT FROM AUTHOR]

Phenomenological models of degradation-relaxation kinetics are considered for jammed systems like structurallyinhomogeneous nanocomposites, exemplified, in part, by screen-printed Cu0.1Ni0.1Co1.6Mn1.2O4 spinel ceramics with conductive Ag and Ag-Pd compound contacts. Nanoinhomogeneities due to Ag or Ag-Pd diffusants in a spinel environment are shown to define the governing kinetics of thermally-induced electrical degradation (at 170oC) obeying non-exponential behavior in negative relative resistance drift. Parameterization of this phenomenon (in part, determination of kineticsresponsible scaling exponent 􀁅) is shown can be simply performed within indirect linear least-square analysis applied to the generalized relaxation function presented in double-logarithmic plotting of variables. Crossover from stretched-exponential (stretching exponent 0<􀁅<1) to compressed-exponential (compressing exponent 􀁅>1) degradation kinetics is revealed in these nanocomposites dependently on contacting diffusant materials, i.e. conductive Ag-Pd (􀁅=0.58) or Ag (􀁅=1.68) compounds. [ABSTRACT FROM AUTHOR]

In this paper we study a general failure that may occur with a certain probability, and its danger may in any way affect the health and functionality of an individual. We introduce the concept of value of risk and further important formulas to this related. Unlike previous papers we use a rather new concept with logarithmic dependence in risk calculation which is accurate and convenient in many situations. In the main part of this paper we derive important relations and results related to this value of risk. All this is illustrated by graphs and tables with important values of the appropriate quantities. [ABSTRACT FROM AUTHOR]

We adapt Bismut's mechanism of the Malliavin Calculus to right invariant big order generator on a Lie group. We use deeply the symmetry in order to avoid the use of the Malliavin matrix. As an application, we deduce logarithmic estimates in small time of the heat kernel. [ABSTRACT FROM AUTHOR]

An arithmetic function is a complex-valued function defined over the positive integers. The set of arithmetic functions equipped with the usual addition and Dirichlet convolution forms a unique factorization domain. Complementing the results in the works of Komatsu et al., the problem of linear dependence over the complex field of arithmetic functions is investigated. Two general criteria are proved. Emphases are placed upon arithmetic functions which are solutions of additive equation, multiplicative equation, exponential equation and logarithmic equation. It is found that i) additive functions are always linearly dependent, ii) exponential functions are always linearly independent, and iii) the situation for logarithmic and multiplicative functions are more complex and conditions for their (in)dependence are derived. [ABSTRACT FROM AUTHOR]

The dynamic force equilibrium equations of the cup of crowned tapered roller bearing under the combined loads condition are established in this paper, considering the centrifugal forces of each roller, the forces of the rib/roller end contact and the contact forces between crowned tapered roller and raceway. The equations are solved based on the Newton iteration method to analysis the dynamic load distribution of crowned tapered roller bearings. The load distribution and contact deformation of tapered roller bearing with three kinds of crowned rollers, such as rollers with straight profile, circular crowned profile and logarithmic crowned profile, are analyzed according to the Palmgren's formula and the numerical method based on influence coefficient method respectively. The results show that the Almgren's formula can be applied to calculation of the dynamic load distribution approximatively, while the numerical method must be used in contact deformation calculation for the crowned tapered roller bearing. [ABSTRACT FROM AUTHOR]

A mathematical description of the method for obtaining gas-dynamic characteristics of a centrifugal compressor stage is proposed, taking into account the control action by varying the rotor speed and the angle of rotation of the guide vanes relative to the "basic" characteristic, if the kinematic and dynamic similitude conditions are not met. The formulas of the correction terms for the non-dimensional coefficients of specific work, consumption and efficiency are obtained. A comparative analysis of the calculated gas-dynamic characteristics of a high-pressure centrifugal stage with experimental data is performed. [ABSTRACT FROM AUTHOR]

Stock prices in the form of time series were analysed using single and multivariate statistical methods. After simple data preprocessing in the form of logarithmic differences, we augmented this single variate time series to a multivariate representation. This method makes use of sliding windows to calculate several dozen of new variables using simple statistic tools like first and second moments as well as more complicated statistic, like auto-regression coefficients and residual analysis, followed by an optional quadratic transformation that was further used for data extension. These were used as a explanatory variables in a regularized logistic LASSO regression which tried to estimate Buy-Sell Index (BSI) from real stock market data. [ABSTRACT FROM AUTHOR]

This paper presents a boundary integral equation method with the adjoint generalized Neumann kernel for conformal mapping of unbounded multiply connected regions. The canonical region is the entire complex plane bounded by an infinite straight slit on the line Im ω = 0 and finite logarithmic spiral slits. Some linear boundary integral equations are constructed from a boundary relationship satisfied by an analytic function on a multiply connected region. These integral equations are uniquely solvable. The kernel involved in these integral equations is the adjoint generalized Neumann kernel. [ABSTRACT FROM AUTHOR]

In this paper we consider the singular integral operator in weighted Lebesgue spaces. Weighted estimates under different parameters up to the best constants obtained for it. [ABSTRACT FROM AUTHOR]

The paper studied the integration of logarithmic singularity problem J(y) = ∬(y¯) log y¯y¯*0dA, where ¯y = (α,β); ¯y0 = (α0;β0); the domain Δ is rectangle Δ = [r1; r2]×[r3; r4]; the arbitrary point ¯ y 2 Δ and the fixed point ¯y0 2 Δ: The given density function z ( ¯ y); is smooth on the rectangular domain Δ and is in the functions class C2;t (Δ): Cubature formula (CF) for double integration with logarithmic singularities (LS) on a rectangle Δ is constructed by applying type (0;2) modified spline function DG(P). The results obtained by testing the density functions z (¯y) as linear and absolute value functions shows that the constructed CF is highly accurate. [ABSTRACT FROM AUTHOR]

In this paper, the Authors establish some new Hermite-Hadamard type inequalities for (β, α; n, m) -logarithmic and (β, α; n, m)-Godunova-Levin-log-convex functions. Some special cases are also discussed. [ABSTRACT FROM AUTHOR]

Inertial-range asymptotic behavior of a vector (e.g., magnetic) field, passively advected by a strongly anisotropic turbulent flow, is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity field is Gaussian, not correlated in time, with the pair correlation function of the form ∝δ (t -t')/kd-1+ξ⊥, where k⊥ = ∣k⊥∣ and k⊥ is the component of the wave vector, perpendicular to the distinguished direction. The stochastic advection-diffusion equation for the transverse (divergence-free) vector field includes, as special cases, the kinematic dynamo model for magnetohydrodynamic turbulence and the linearized Navier-Stokes equation. In contrast to the well known isotropic Kraichnan's model, where various correlation functions exhibit anomalous scaling behavior with infinite sets of anomalous exponents, here the dependence on the integral turbulence scale L has a logarithmic behavior: instead of powerlike corrections to ordinary scaling, determined by naive (canonical) dimensions, the anomalies manifest themselves as polynomials of logarithms of L. [ABSTRACT FROM AUTHOR]

This study aims to investigate the implied adjusted volatility functions using the different Leland option pricing models and to assess whether the use of the specified implied adjusted volatility function can lead to an improvement in option valuation accuracy. The implied adjusted volatility is investigated in the context of Standard and Poor/Australian Stock Exchange (S&P/ASX) 200 index options over the course of 2001-2010, which covers the global financial crisis in the mid-2007 until the end of 2008. Both in- and out-of-sample resulted in approximately similar pricing error along the different Leland models. Results indicate that symmetric and asymmetric models of both moneyness ratio and logarithmic transformation of moneyness provide the overall best result in both during and postcrisis periods. We find that in the different period of interval (pre-, during and post-crisis) is subject to a different implied adjusted volatility function which best explains the index options. Hence, it is tremendously important to identify the intervals beforehand in investigating the implied adjusted volatility function. [ABSTRACT FROM AUTHOR]

The aim of this research work is to conduct curve fitting using mathematical equations that relate location of the hydrocarbon (HC) at different depth to different frequencies. COMSOL MultiPhysics software was used to generate models of the seabed logging technique which consists of air, sea water, sediment and HC layer. Seabed Logging (SBL) is a technique to find the resistive layers under seabed by transmitting low frequency of EM waves through sea water and sediment. As HC is known to have high resistivity which is about 30-500Ωm, EM waves will be guided and reflected back and detected by the receiver that are placed on the seafloor. In SBL, low frequency is used to obtain greater wavelength which allows EM waves to penetrate at longer distance and each frequency used has different skin depth. The frequencies used in this project were 0.5Hz, 0.25Hz, 0.125Hz and 0.0625Hz and the depths of the HC were varied from 1000m to 3000m with increment of 250m. Data generated from the simulations using COMSOL software was extracted for the set up with and without HC and few trend lines were developed and R² were calculated for each equation and curve. The calculated R² were compared between data with HC to no HC at each depth and it was found that the calculated R² values were very well fitted for deeper HC depth. This indicates that as depth of HC is higher, it is difficult to distinguish data with and without HC presence; and perhaps a new technique can be explored. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce two new subclasses of the function class S of bi-univalent functions involving polylogarithm functions defined in the open unit disc U=:{z:z...C,|z|<1} . The estimates on the coefficients the rest of this text. |a2| and |a3| for functions in these new subclasses of the function class S are obtained in our investigation. [ABSTRACT FROM AUTHOR]

In this paper, we report data on PS foamed at 100 °C after CO2 saturation at 10 MPa in a new physical foaming batch that achieves pressure drop rates up to 120 MPa/s. Results show how average cell size of the foam nicely fit a linear behavior with the pressure drop rate in a double logarithmic plot. Furthermore, foam density initially decreases with the pressure drop rate, attaining a constant value at pressure drop rates higher than 40 MPa/s. Interestingly, furthermore, we observed that the shape of the pressure release curve has a large effect on the final foam morphology, as observed in tests in which the maximum pressure release rate was kept constant but the shape of the curve changed. These results allow for a fine tuning of the foam density and morphology for specific applications. [ABSTRACT FROM AUTHOR]

Three common methods of determining criteria weights using the Analytic Hierarchy Process (AHP) are extent analysis, logarithmic least square method (LLSM) and Lambda-Max. Lambda-Max criteria weights determination method uses pair wise comparison of criteria considered. Studies have shown that Lambda-Max is a preferred criteria weight determination method since it involves lesser computation with consistent results of precise criteria weights generated. In this paper the criteria weights of four factors impacting the Melt Flow Index of degradable plastics are calculated using Lambda-Max method. The input factors (criteria) are the percentages by mass of polyethylene, oil palm biomass, palm olein and starch used in the formulation of degradable plastics. The criteria weights are calculated using Lambda-Max based on input given by four experts. The finding indicates the feasibility of using Lambda-Max method in criteria weight determination for determining the impact of four factors in the formulation of degradable plastics as reflected by the consistency control index value calculated. [ABSTRACT FROM AUTHOR]

Autocorrelated process control is common in today's modern industrial process control practice. The current practice of autocorrelated process control is to eliminate the autocorrelation by using an appropriate model such as Box-Jenkins models or other models and then to conduct process control operation based on the residuals. In this paper we show that many time series are governed by a geometric Brownian motion (GBM) process. Therefore, in this case, by using the properties of a GBM process, we only need an appropriate transformation and model the transformed data to come up with the condition needs in traditional process control. An industrial example of cocoa powder production process in a Malaysian company will be presented and discussed to illustrate the advantages of the GBM approach. [ABSTRACT FROM AUTHOR]

We propose and motivate an expanded version of the logarithmic score for forecasting distributions, termed the Total Log score. It incorporates the usual logarithmic score, which is recognised as incomplete and has been mistakenly associated with the likelihood principle. The expectation of the Total Log score equals the Negentropy plus the Negextropy of the distribution. We examine both discrete and continuous forms of the scoring rule, and we discuss issues of scaling for scoring assessments. The analysis suggests the dual tracking of the quadratic score along with the usual log score when assessing the qualities of probability distributions. An application to the sequential scoring of forecast distributions for the daily rate of stock returns displays the usefulness of the proposal. [ABSTRACT FROM AUTHOR]

Self-similarity properties of fractal structures and logarithmic spiral are related to quantum dissipative dynamics, squeezed coherent states and noncommutative geometry in the plane. [ABSTRACT FROM AUTHOR]

Recently, many documents or messages from an organization need to be signed by more than one person. For that reason, many threshold signatures based on various problems in number theory have been developed. In this paper, a threshold signature scheme based on two most popular number theory problems, namely factoring and discrete logarithms, was proposed. The advantage of this new scheme is based on the fact that it is very hard to solve both factoring and discrete logarithms problems simultaneously. This scheme is also shown secure against several attacks and requires a reasonable time complexity in both signing and verifying phase. [ABSTRACT FROM AUTHOR]

The authors show how we may, through the use of some extended product expressions for the Gamma function and some detailed work on the characteristic functions of the negative logarithm of the product of particular independent Beta random variables, whose second parameters are rational, obtain in a single shot (i) simple expressions for both the probability density and cumulative distribution functions of this product, as well as, concomitantly (ii) very simple and easy to compute alternative finite form expressions for instances of the Meijer G and Fox H functions. These alternative expressions are based on the expressions for the probability density and cumulative distribution functions of the Generalized Integer Gamma distribution and they are not used or recognized by the available software. [ABSTRACT FROM AUTHOR]

Fueter's construction of revolving planar mappings f around the real axis, developed by Leutwiler in 1992, is interpreted as a mathematical model for the meridional velocity fields in an axially symmetric inhomogeneous medium. We characterize new geometric and applied properties of some typical functions of the reduced quaternionic variable in the framework of generalizations of conformal mappings of the second kind in R3. The ñ-th power and new generalizations of the classical Joukowski transformation in the form of functions of the reduced quaternionic variable are studied. New velocity potentials in the form of [lowercase_phi_synonym]-harmonic potential functions are given explicitly. Some unknown properties of the logarithmic function and the exponential function of the reduced quaternionic variable are demonstrated. In contrast to theory of functions of a complex variable, in modified quaternionic analysis the Hessian matrix of each potential function has variable trace in R3. The Hessian matrix is interpreted as the deformation rate tensor, which can be decomposed into its spherical part and its deviatoric part with zero trace. [ABSTRACT FROM AUTHOR]

This paper presents a technique for maximum power point tracking (MPPT) of a concentrating photovoltaic system using cell level power optimization. Perturb and observe (P&O) has been a standard for an MPPT, but it introduces a tradeoff between the tacking speed and the accuracy of the maximum power delivered. The P&O algorithm is not suitable for a rapid environmental condition change by partial shading and self-shading due to its tracking time being linear to the length of the voltage range. Some of researches have been worked on fast tracking but they come with internal ad hoc parameters. In this paper, by using the proposed unbounded binary search algorithm for the MPPT, tracking time becomes a logarithmic function of the voltage search range without ad hoc parameters. [ABSTRACT FROM AUTHOR]

In this tutorial we review the essential arguments behing entropic inference. We focus on the epistemological notion of information and its relation to the Bayesian beliefs of rational agents. The problem of updating from a prior to a posterior probability distribution is tackled through an eliminative induction process that singles out the logarithmic relative entropy as the unique tool for inference. The resulting method of Maximum relative Entropy (ME), includes as special cases both MaxEnt and Bayes' rule, and therefore unifies the two themes of these workshops-the Maximum Entropy and the Bayesian methods-into a single general inference scheme. [ABSTRACT FROM AUTHOR]

Here the central figure is the logarithm function because its numerous properties in mathematics and its interventions in information theory, statistics, acoustics, functional equations, ... Among all the possibilities of the logarithm and also the exponential, here we introduce a new statistic named the expo-dispersion well suited for logarithmic data as the levels of magnitudes. It is a statistic which characterizes the dispersion of data as do variance and entropy, and they have many common behaviours and properties. [ABSTRACT FROM AUTHOR]

In this article, we investigate the issue of the selection of eye movements in a free-eye Multiple Object Tracking task. We propose a Bayesian model of retinotopic maps with a complex logarithmic mapping. This model is structured in two parts: a representation of the visual scene, and a decision model based on the representation. We compare different decision models based on different features of the representation and we show that taking into account uncertainty helps predict the eye movements of subjects recorded in a psychophysics experiment. Finally, based on experimental data, we postulate that the complex logarithmic mapping has a functional relevance, as the density of objects in this space in more uniform than expected. This may indicate that the representation space and control strategies are such that the object density is of maximum entropy. [ABSTRACT FROM AUTHOR]

The functional equation af(xy)+bf(x)f(y)+cf(x+y)+d(f(x)+f(y)) = 0 whose shape contains all the four well-known forms of Cauchy's functional equation is solved for solutions which are functions having the positive reals as their domain. This complements an earlier work of Dhombres in 1988 where the same functional equation was solved for solutions whose domains contain zero, which leaves out the logarithmic function. Here not only the logarithmic function is recovered but the analysis is entirely different and is based on solving appropriate difference equations. [ABSTRACT FROM AUTHOR]

The time discretization of semilinear parabolic problems requires integrators that treat the stiff part in an implicit way. Traditionally, linearly implicit methods had been used for this purpose. More recently, exponential integrators proved to be competitive for this kind of problems. In this short note, we will put emphasis on methods that linearize the problem along the numerical trajectory. We will show that the error analysis can be carried out in the framework of logarithmic matrix norms which gives rise to convergence results that are independent of the spatial grid size. [ABSTRACT FROM AUTHOR]

Refinements, generalizations and new results concerning Hadamard’s inequality for log convex functions are achieved. [ABSTRACT FROM AUTHOR]

This is a summarized version of the forthcoming paper [11]. Let q be a complex parameter with |q|<1. We shall study in this paper asymptotic aspects when q→1 of certain general classes of q-integral and q-differential operations given in (1.5) and (1.6) below respectively; this leads us to establish complete asymptotic expansions for their iterated extensions (Theorems 1 and 2) under fairly generic situations (Theorem 3). Several applications of of our main formulae (2.4) and (2.9) are further given for the generalized Lerch zeta-function defined by (3.3) (Theorems 4–6 and Corollary 6.1), the q-factorials (Corollary 4.1), q-analogues of the exponential (Corollary 4.2), the binomial (Corollary 4.3), and the poly-logarithmic functions (Corollaries 4.4 and 5.1). [ABSTRACT FROM AUTHOR]

We propose a 2D study of jamming at the outlet of a silo in the metastable state by means of the nonsmooth contact dynamics method. The jamming problem in this geometry can be mapped into the avalanche problem on a granular slope. In this analogy, the size of the opening plays the same role as the slope angle whereas the number of passing particles between two jams corresponds to the avalanche size. We use a simple protocol to break the arch and thus trigger a new avalanche every time an arch is formed. We find that the probability density of avalanche size scaled by the mean avalanche size is a decreasing exponential function independent of the opening. The mean avalanche size increases with the opening and it diverges as a critical opening is approached. This transition to steady flow where the jamming probability vanishes, bears close analogy to transition to steady flow on an inclined plane at the maximum angle of stability. We also present a simple model of passing events as an uncorrelated process. This model provides an excellent fit to the avalanche statistics. [ABSTRACT FROM AUTHOR]

We present arithmetical property concerning with hypergeometric function of Gauss which will be useful to obtain Diophantine approximations of the values of the function. As is seen in [2], in quantitative theory of linear forms in logarithms, not only exponential function but also logarithmic function is directly used to construct auxiliary functions. We revisit the fact that the values of Gauss' hypergeometric function are viewed as values of abelian logarithmic function. We give here a related estimate for such functions. [ABSTRACT FROM AUTHOR]

We summarize and classify results on the evaluations and expressions in closed from of various reciprocal sums of Fibonacci numbers and Lucas numbers using classical functions, such as theta functions, complete elliptic integrals of the first and second kind, Lambert series, and q-exponential functions. In the final section we give closed form expressions of series of rational functions and evaluate series involving Fibonacci and Lucas numbers. [ABSTRACT FROM AUTHOR]

The problem of the construction of Diophantine m-tuples, i.e. sets with the property that the product of any two of its distinct elements is one less then a square, has a very long history. In this survey, we describe several conjectures and recent results concerning Diophantine m-tuples and their generalizations. [ABSTRACT FROM AUTHOR]

The capture and emission time constants dependence on drain current for constant gate voltage and variable drain voltage show that probability for charge carrier capture decreases with increasing lateral electric field while emission process is independent on lateral field intensity. We have performed analyses of SiO2 gate insulating layer from VA characteristics measured in wide temperature range (gate electrode area 1.5 μm2, insulating layer thickness 6 nm. Leakage current in reverse mode of n-MOS sample (for gate electrode negative) is for applied voltage lower than 1 V exponential function of applied voltage with saturation current I0 = (1–3)×10-16 A and ideality factor near to 1. Saturation current value corresponds to Schottky barrier high about 1.2 eV. We suppose that in SiO2 gate insulating layer and on the interface Si-SiO2 there are oxygen vacancies and interstitials. High density of overlapping energy localized states creates in SiO2 impurity conduction band about 1.2 eV above the Si conduction band. Between channel and interface Si-SiO2 localized states exists g-r stochastic exchange of electrons, which is a source of 1/f noise. Reducing the density of interface states by plasma oxidation leads to 1/f noise spectral density lowering. There exists electron exchange by tunnelling between interface Si-SiO2 localized states and traps localized in gate insulating layer about lnm from channel. These quantum transitions are sources of RTS noise. Electron from channel trap can tunnel to interface Si/SiO2 localized state or it can enter through SiO2 impurity conductivity band to gate electrode by thermionic emission. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

In R-parity conserving supersymmetric (SUSY) models, sleptons are produced in pairs at hadron colliders. We show that measurements of the longitudinal single-spin asymmetry at possible polarization upgrades of existing colliders allow for a direct extraction of the slepton mixing angle. A calculation of the transverse-momentum (qT) spectrum shows the importance of resummed contributions at next-to-leading logarithmic (NLL) accuracy in the small and intermediate qT-regions and little dependence on unphysical scales and non-perturbative (NP) contributions. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

The initial analyses of the next-to-leading logarithmic corrections to the BFKL kernel were very discouraging. Encouraged by the success of new methods in the analysis of the BFKL equation at full NLL accuracy we demonstrate in this talk how some of the initial conclusions were based on a breakdown of the tools used in the analysis rather than the framework itself. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]

Nanostructured CoCu granular alloys CoxCu1-x (x ≤ 0.3) have been prepared by chemical reduction method using NaBH4 as a reducing agent. Electronic transport properties are studied in the temperature range 4-300 K. Resistance exhibits a metallic behavior below room temperature and draws a minimum near 20 K in all the samples except in Co0.3Cu0.7. This low temperature resistivity minimum diminishes with applied magnetic field. There is also a logarithmic temperature dependence of resistivity at temperatures below 20 K. This phenomenon indicates a Kondo-like scattering mechanism involving magnetic Co impurity spin clusters in Cu host. [ABSTRACT FROM AUTHOR]

We predict the energy profiles of light-quark and gluon jets in the framework of perturbative QCD. Resumming large logarithmic contributions to all orders in the coupling constant, our predictions are shown to agree well with Tevatron CDF and Large-Hadron-Collider CMS data. We also extend our resummation formalism to the invariant mass distributions of light-quark and gluon jets produced in hadron collisions. [ABSTRACT FROM AUTHOR]

Logarithmic function has been designed on basis of multiplicative normalization and then its testing is been done using tetraMAX. It is observed that 7050 possible faults can be there in the design and tetraMAX ATPG can provide test coverage of 99.29%. Using design compiler .db file is generated which is used for functional verification of the design with respect to RTL design. Compare points are shown by cone views of the design. [ABSTRACT FROM AUTHOR]

We construct a symmetric effective Hamiltonian which governs the behavior of scattering amplitudes in QCD at high energy in the leading logarithmic approximation. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]