Decimal Digits Research Articles

Some Features of the construction of a family of atomic radial basis functions Plop r,a (x1,x2)

A lot of methods for solving boundary value problems using arbitrary grids, such as SDI (scattered data interpolation) and SPH (smoothed particle hydrodynamics), use families of atomic radial basis functions that depend on parameters to improve the accuracy of calculations. Functions of this kind are commonly called "shape functions". When polynomials or polynomial splines are used as such functions, they are called "basis functions". The term "radial" means that the carrier of the function is a disk or layer. The term "atomic" means that the support of the function is limited, ie the function is finite. In most cases, the term "finite" is used in English-language publications. The article presents an algorithm for constructing such a function, which is the solution of the functional-differential equation where - circle of radius r: , and . The function generated by this equation has two parameters: r and . Variation of these parameters allows to reduce the error in the calculations of the Poisson boundary value problem by several times. The theorem on the existence of such an unambiguous function is proved in the article. The proof of the theorem allows us to construct one-dimensional Fourier transform of this function in the form , where . Previously, function was calculated using its Taylor approximation (at ), and at – using the asymptotic Hankel approximation of the function . Thus in a circle of a point a fairly large error was found. Therefore, the calculation of the function in the range was carried out by Chebyshev approximation of this function in the range . Chebyshev coefficients (calculated in the Maple 18 system with an accuracy of 26 decimal digits) and the range were chosen by an experiment aimed at minimizing the overall error in calculating of the function . Thanks to the use of the Chebyshev approximation, the obtained function has more than twice less error than calculated by the previous algorithm. Arbitrary value of the function is calculated using a six-point Aitken scheme, which can be considered (to some extent) a smoothing filter. The use of Aitken's six-point scheme introduces an error equal to 6% of the total function calculation error , but helps to save a lot of time in the formation of ARBF in solving boundary value problems using the method of collocation.

On generalizing happy numbers to fractional-base number systems

Let n be a positive integer and S2(n) be the sum of the squares of its decimal digits. When there exists a positive integer k such that the k-th iterate of S2 on n is 1, i.e., S2k(n)=1, then n is called a happy number. The notion of happy numbers has been generalized to different bases, different powers and even negative bases. In this article we consider generalizations to fractional number bases. Let Se,p∕q(n) be the sum of the e-th powers of the digits of n base pq. Let k be the smallest nonnegative integer for which there exists a positive integer m>k satisfying Se,p∕qk(n)=Se,p∕qm(n). We prove that such a k, called the height of n, exists for all n, and that, if q=2 or e=1, then k can be arbitrarily large.

Enhancing PIGPEN Image Steganography Method by Using Zigzag Scanning

Steganography is the art and science of writing hidden messages in such a way that no one suspects the existence of the message, a form of security through obscurity. Many different carrier file formats can be used, but digital images are the most popular because of their frequency on the internet. In this paper explains the PIGPEN image steganography technique which modifies the secret message itself not the technique of embedding. This technique represents the secret message characters by two decimal digits only not three decimal digits as ASCII encoding. So, it can save one third of the required space for embedding the message in an image. The PIGPEN technique will be enhanced by using the zigzag scanning to increase the security and achieves higher visual quality as indicated by the high peak signal-to-noise ratio (PSNR) in spite of hiding a large number of secret bits in the image.

The Multiplication Method with Scaling the Result for High-Precision Residue Positional Interval Logarithmic Computations

Introduction. The solution of the simulation problems critical to rounding errors, including the problems of computational mathematics, mathematical physics, optimal control, biochemistry, quantum mechanics, mathematical programming and cryptography, requires the accuracy from 100 to 1 000 decimal digits and more. The main lack of high-precision software libraries is a significant decrease of the speed-in-action, unacceptable for practical problems, in particular, when performing multiplication. A way to increase computation performance over very long numbers is using the residue number system. In this work, we discuss a new fast multiplication method with scaling the result using original hybrid residue positional interval logarithmic floating-point number representation. Materials and Methods. The new way of the organizing numerical information is a residue positional interval logarithmic number representation in which the mantissa is presented in the residue number system, and information on an absolute value (the characteristic) in the interval logarithmic number system that makes it possible to accelerate performance of comparison and scaling is developed to increase the speed of calculations; to compare modular numbers, the provisions of interval analysis are used; to scale modular numbers, the properties of the logarithmic number system and approximate interval calculations using the Chinese reminder theorem are used. Results. A new fast multiplication method of floating-point residue-represented numbers is developed and patented; the authors evaluated the developed method speed-in action, compared the developed method with classical and pipelined multiplication methods of long numbers. Discussion and Conclusion. The developed method is 2.4–4.0 times faster than the pipelined multiplication method, and is 6.4–12.9 times faster than classical multiplication methods.

Temperature extreme records: World Meteorological Organization metrological and meteorological evaluation of the 54.0°C observations in Mitribah, Kuwait and Turbat, Pakistan in 2016/2017

AbstractA World Meteorological Organization (WMO) committee officially evaluated temperature record extremes of 54.0°C at two locations, one in Mitribah, Kuwait on July 21, 2016 and a second in Turbat, Pakistan on May 28, 2017. The committee agreed that quantity and quality of documentation of both observations were excellent. Additional metrological testing of the equipment focused on three aspects: the calibration of both thermometers, an effort to estimate the factors influencing the measurements and a direct comparison of the two thermometers when exposed simultaneously to 54°C. The metrological analysis's conclusion for the Mitribah value is a temperature estimated to be 53.87°C with an expanded uncertainty of ±0.08°C. Correspondingly, for the Turbat value the temperature is estimated to be 53.72°C with an expanded uncertainty of ±0.40°C. Following that analysis, the committee recommended acceptance of the calibrated observations to the first decimal digit such that the Mitribah observation is accepted as 53.9 ± 0.1°C and the Turbat as 53.7 ± 0.4°C. The Mitribah, Kuwait temperature is now accepted by the WMO as the highest temperature ever recorded for Asia (WMO RA II) and the two observations are the third (tied within uncertainty limits) and fourth highest WMO‐recognized temperature extremes and, significantly, they are the highest, officially recognized temperatures to have been recorded in the last 76 years. This evaluation has involved the most extensive temperature extremes analysis ever to be undertaken by an international evaluation committee of the WMO CCl Archive of Weather and Climate Extremes.

Choptuik’s Critical Spacetime Exists

About twenty years ago, Choptuik studied numerically the gravitational collapse (Einstein field equations) of a massless scalar field in spherical symmetry, and found strong evidence for a universal, self-similar solution at the threshold of black hole formation. We prove rigorously the existence of a real analytic solution, that we interpret as the solution observed by Choptuik. Our construction covers an open neighborhood of the past light cone of the singularity. The proof is computer assisted. Starting from an explicit approximate solution, we show that nearby there is a true solution. The source code and a high precision data file (about 80 significant decimal digits, with rigorous error bounds) are included. We do not study perturbations.

High-accuracy numerical calculations of the bound states of a hydrogen atom in a constant magnetic field with arbitrary strength

We develop a simple and effective method for solving the Schrödinger equation of a hydrogen atom in a constant magnetic field with arbitrary strength. Energies are obtained not only for the ground and low-lying states but also for highly excited states with precision from 12 up to 20 decimal digits. The calculations are performed for an entire range of magnetic field intensity up to 9.4×108 Tesla, the strongest field ever observed. The strong point of the development of the method is the construction of an anharmonic oscillator model for a hydrogen atom in a constant magnetic field via the Kustaanheimo–Stiefel transformation. This model allows the use of purely algebraic calculations and the Feranchuk–Komarov (FK) operator method for effectively solving the Schrödinger equation. The advantages of the basis set in this work are also discussed to extend its application to other problems, such as multi-electron atoms in a constant magnetic field. We also provide a program written by FORTRAN for the solutions mentioned above. Program summaryProgram Title: CHAMFProgram Files doi:http://dx.doi.org/10.17632/s5shscgfcj.1Licensing provisions: BSD 3-clauseProgramming language: FORTRAN77Nature of problem: The Schrödinger equation for a hydrogen atom in a magnetic field is rewritten into that of a four-dimensional anharmonic oscillator by using the Kustaanheimo–Stiefel transformation. The later has a structure more convenient for applying the algebraic method based on annihilation and creation operators. Therefore, the FK operator method [1] can be applied for obtaining high-accuracy numerical solutions which means the obtained energies converge to a given precision (up to twenty decimal digits in this work). The method is developed for an entire range of magnetic field intensity up to 9.4×108 Tesla and for not only ground state but also highly excited states.Solution method: The FK operator method is modified and used for the high-accuracy numerical solutions. This method combines with the algebraic technique which is useful for calculating all the needed matrix elements. Thus, the Schrödinger equation becomes the symmetric generalized eigenvalue problem which can be solved by the subroutine dsygvx.f of the LAPACK library [2]. For the better accuracy with quadruple precision, we modify this subroutine and its dependence with using the real*16 number instead of the real*8. Moreover, a free parameter introduced by the FK operator method can be used for increasing the speed of convergence. The optimal choice of this free parameter is implemented in the program.Additional comments including restrictions and unusual features: Operating system: Linux. RAM: at least 1 GByte per core. The gfortran compiler is recommended for this program. The running time is from a centisecond to a few minutes depending on the required precision. However, for the super-strong magnetic fields (γ≥200), the running time may reach to two hours for the precision of twelve decimal digits, and RAM is needed to be at least 60 GB.[1] I. Feranchuk, A. Ivanov, Van-Hoang Le, A. Ulyanenkov, Non-perturbative Description of Quantum Systems, Springer, Switzerland, 2015. doi:10.1007/978-3-319-13006-4.[2] Netlib.org. LAPACK: Linear Algebra PACKage, Subroutine dsygvx.f. URL http://www.netlib.org/lapack/lapack-3.1.1/html/dsygvx.f.html

Architectures for multiple constant decimal multiplication

Due to the increasing demand for decimal calculations in the business, financial and economic world, decimal arithmetic circuits have been much considered by system designers. This is mainly because, these applications heavily depend on decimal arithmetic since the results must match exactly those obtained by human calculations. While decimal multiplication is one of the most frequent and complex-to-implement decimal operations, the special case of constant decimal multiplication is widely used in the economic and financial applications. In this paper, we propose two ideas, named “Constant Decimal TCSD” (CDT) and “Constant Decimal DDDS” (CDD), and their hardware implementations for realizing multiple constant decimal multiplication. In the CDT and CDD architectures, the partial products are generated using a set of positive multiplicand multiples coded in2′s complement signed-digit format (TCSD) and binary coded decimal (BCD), respectively. We also present two new (3:1) compressors to reduce the number of partial products in both designs, one based on a new Double Decimal Digit Set (DDDS), which is not only self-complementing but also its redundancy, allows carry-free addition. Finally, a redundant to non-redundant converter recodes the TCSD and DDDS product to BCD in the first and second schemes, respectively. Hardware synthesis evaluation shows that compared to the most recent 16 × 16 decimal multipliers, delay, area, power consumption and PDP of the proposed multiple constant multipliers improve up to 57%, 89%, 93% and 97%, respectively.

Toward the theory of the Yukawa potential

Using three different approaches Perturbation Theory (PT), the Lagrange Mesh Method (LMM), and the variational method, we study the low-lying states of the Yukawa potential. First orders of PT, in powers of the screening parameter, are calculated in the framework of the non-linearization procedure. It is found that the Padé approximants to PT series together with the LMM provide highly accurate values of energy and the positions of the radial nodes of the wave function. The most accurate results, at present, of the critical screening parameters for some low-lying states and the first coefficients in the expansion of the energy at the critical parameter are presented. A locally accurate and compact trial function for the eigenfunctions of the low-lying states is discovered. This function used as a zeroth order entry in PT leads to energies as precise as those of Padé approximants and LMM. Finally, a compact analytical expression for the energy, that reproduces at least 6 decimal digits in the entire physical range of the screening parameter, is found.

TFmix: A high-precision implementation of the finite-temperature Thomas–Fermi model for a mixture of atoms

In this work we present a TFmix code intended for numerical calculation of the thermal part of electronic thermodynamic properties of a mixture of elements by the finite-temperature Thomas–Fermi model. The code is based on analytical models for both first and second derivatives of Helmholtz thermodynamic potential. All numerical calculations are made within a controlled high accuracy: tests for thermodynamic consistency give at least 11 coinciding decimal digits. The code calculates thermodynamic functions on a regular grid of isotherms and isochores; at each grid point some extensive parameters and the number of free electrons are output both for the whole mixture and for each component. Other extensive or intensive thermodynamic properties, including pressure, entropy, isochoric and isobaric heat capacities, isothermal and adiabatic sound velocities can be easily calculated from the information available at each grid point. Several unit systems are provided for convenience. A cross-platform graphical user interface is developed to simplify the use of the code. Program summaryProgram Title: TFmix, version 1.0Program Files doi:http://dx.doi.org/10.17632/mc3vj77jfn.1Licensing provisions: GPLv3Programming language: C, PythonNature of problem: Any substance consists of elements so its equation of state contains a contribution of electronic gas. Thermodynamics of the electronic gas in a mixture of ions and electrons has been studied in many approaches. Thermodynamic properties of a uniform ideal electron gas can be calculated using the well-known analytical model of Fermi-gas. On the other hand, models of electron gas which take into account interaction effects are quite complicated and require sophisticated computational techniques. Even a simplified semiclassical Thomas–Fermi model is based upon the numerical solution of a non-linear boundary problem. Two main issues of the Thomas–Fermi model restrict its usage: uncontrolled accuracy of calculated thermodynamic functions (especially second derivatives of a thermodynamic potential), and unphysical behavior of the model at relatively low temperatures.Solution method: Each atom in the mixture is surrounded by a spherical cell. The radii of the cells are fitted to equalize the chemical potentials of all atoms. A guaranteed accuracy of first derivatives of the thermodynamic potential is provided by a transformation of integrals over the Thomas–Fermi potential to a system of differential equations. One of equations in the system is the Thomas–Fermi equation. Second derivatives of the thermodynamic potential are calculated similarly with the only difference that a corresponding derivative of the Thomas–Fermi equation is used in the system of differential equation. To avoid the unphysical behavior of the Thomas–Fermi model at low temperatures we extract a thermal contribution to thermodynamic properties which vanishes at zero temperature. To eliminate the error which appears from the subtraction of the cold part at low temperatures we use asymptotic expressions for thermodynamic functions and the Thomas–Fermi equation. The code calculates regular tables of thermodynamic functions on a grid of isotherms and isochores including second derivatives of a thermodynamic potential. This information is necessary for astrophysical applications, for continuum mechanics simulation of processes in plasma and for the creation of wide-range equations of state. A graphical user interface is provided with the code and allows to specify input parameters, to perform calculations and to plot the results.Additional comments including restrictions and unusual features: GSL library version 1.16 or 2.x is required for compilation; matplotlib Python library is required to run the graphical user interface.

Complex eigenvalues of slotted arbitrary cylindrical cavities: Sound-soft elliptic cavity with variably placed longitudinal slit.

A generalization of the rigorous method of regularization is implemented to calculate the complex eigenvalues for a two dimensional arbitrarily shaped acoustically soft cavity with a longitudinal slit. The problem is reduced to the finding of non-trivial solutions of the coupled homogeneous well-conditioned Fredholm second kind infinite systems of linear algebraic equations that are solved numerically by the truncation method. The guaranteed fast convergence of the solution of the truncated system to the exact solution allows one to achieve any pre-determined accuracy by proper choice of truncation number. Formally, the complex eigenvalues coincide with the complex roots of the characteristic equation of the truncated infinite system. All calculations are performed with an accuracy of six significant decimal digits. The algorithm is free from limitations on the slit width, frequency band, and slit location along the bounding contour of a cavity. As an example, the spectrum of the complex eigenvalues for open elliptic cavity with moveable longitudinal slit is accurately investigated for various ellipse eccentricities, including the case of degenerated elliptic cavity-circular cavity. The slit width varies from zero value (closed cavity) to open semi-elliptic cavity.

Do [formula omitted] lepton branching fractions obey Benford’s Law?

According to Benford’s law, the most significant digit in many datasets is not uniformly distributed, but obeys a well defined power law distribution with smaller digits appearing more often. Among one of the myriad particle physics datasets available, we find that the leading decimal digit for the τ lepton branching fraction shows marginal disagreement with the logarithmic behavior expected from the Benford distribution. We quantify the deviation from Benford’s law using a χ2 function valid for binomial data, and obtain a χ2 value of 16.9 for nine degrees of freedom, which gives a p-value of about 5%, corresponding to a 1.6σ disagreement. We also checked that the disagreement persists under scaling the branching fractions, as well as by redoing the analysis in a numerical system with a base different from 10. Among all the digits, ‘9’ shows the largest discrepancy with an excess of 4σ. This discrepancy is because the digit ‘9’ is repeated for three distinct groups of correlated modes, with each group having a frequency of two or three, leading to double-counting. If we count each group of correlated modes only once, the discrepancy for this digit also disappears and we get pristine agreement with Benford distribution.

A novel design of a ternary coded decimal adder/subtractor using reversible ternary gates

In recent years, an outstanding amount of interest has been given to reversible circuits. Their applications in distinctive fields that include digital circuit design with low-power consumption, computational circuit design in quantum computer and DNA-based computations are of high significance. Because of advantages of ternary circuits over binary circuits, such as reducing the complexity of interconnects, smaller chip area and reducing the number of quantum cells for the quantum circuit, ternary logic is suggested to construct new compact circuits. Also, in quantum technology, without any restrictions with the same physical phenomena that binary circuits are implemented, new circuits can be implemented in ternary logic. Circuit design for decimal calculations, which includes addition and subtraction of decimal numbers, has continually been the interest of digital circuit designers. In reversible ternary computation, the reversible circuits for decimal calculations have been less studied. In this paper, a reversible ternary adder/subtractor circuit for the addition/subtraction of decimal digits in radix three is proposed. Ternary Coded Decimal (TCD) codes are used to display decimal inputs and outputs. In circuit implementation, first by removing the unused inputs and outputs in the required ternary adders in the TCD Adder, three blocks of reversible 3-qutrit ternary adder with the quantum cost of 29, 22, 14 and constant inputs of 0, 1, and 0 were presented, then an optimal circuit for the TCD detector with a quantum cost of 16 was introduced. The proposed TCD detector has 23% improvement in quantum cost as compared to the existing design. By applying these in the design of the reversible TCD Adder, a more optimal reversible TCD Adder circuit than the existing design was presented resulting in a 31% improvement in quantum cost and 58% improvement in the number of constant inputs. Finally, decimal 9's complement circuit for the subtraction of two decimal numbers was proposed. In the proposed TCD Adder/Subtractor, the new proposed TCD Adder and decimal 9's complement circuits were used. To realize all proposed circuits, 1-qutrit shift gates and 2-qutrit Muthukrishnan-Stroud gates, which are realized in ion-trap technology in quantum computers, were used.

Identifying inaccuracy of MS Project using system analysis

The problem encountered in project owner’s financial accounting report is the difference in total project costs of MS Project to the Indonesian Standard (Standard Indonesia Standard / Cost Estimating Standard Book of Indonesia). It is one of the MS Project problems concerning to its cost accuracy, so cost data cannot be used in an integrated way for all project components. This study focuses on finding the causes of inaccuracy of the MS Projects. The aim of this study, which is operationally, are: (i) identifying cost analysis procedures for both current methods (SNI) and MS Project; (ii) identifying cost bias in each element of the cost analysis procedure; and (iii) analysing the cost differences (cost bias) in each element to identify what the cause of inaccuracies in MS Project toward SNI is. The method in this study is comparing for both the system analysis of MS Project and SNI. The results are: (i) MS Project system in Work of Resources element has limitation for two decimal digits only, have led to its inaccuracy. Where the Work of Resources (referred to as effort) in MS Project represents multiplication between the Quantities of Activities and Requirements of resources in SNI; (ii) MS Project and SNI have differences in the costing methods (the cost estimation methods), in which the SNI uses the Quantity-Based Costing (QBC), meanwhile MS Project uses the Time-Based Costing (TBC). Based on this research, we recommend to the contractors who use SNI should make an adjustment for Work of Resources in MS Project (with correction index) so that it can be used in an integrated way to the project owner’s financial accounting system. Further research will conduct for improvement the MS Project as an integrated tool toward all part of the project participant.

Calculation of the Fine-Structure Constant

The fine-structure constant α [1] is a constant in physics that plays a fundamental role in the electromagnetic interaction. It is a dimensionless constant, defined as: (1) being q the elementary charge, e0 the vacuum permittivity, h the Planck constant and c the speed of light in vacuum. The value shown in (1) is according CODATA 2014 [2]. In this paper, it will be explained that the fine-structure constant is one of the roots of the following equation: (2) being e the mathematical constant e (the base of the natural logarithm). One of the solutions of this equation is: (3) This means that it is equal to the CODATA value in nine decimal digits (or the seven most significant ones if you prefer). And therefore, the difference between both values is: (4) This coincidence is higher in orders of magnitude than the commonly accepted necessary to validate a theory towards experimentation. As the cosine function is periodical, the Equation (2) has infinite roots and could seem the coincidence is just by chance. But as it will be shown in the paper, the separation among the different solutions is sufficiently high to disregard this possibility. It will also be shown that another elegant way to show Equation (2) is the following (being i the imaginary unit): (5) having of course the same root (3). The possible meaning of this other representation (5) will be explained.

Highly Accurate Recognition of Handwritten Arabic Decimal Numbers Based on a Self-Organizing Maps Approach

Handwritten numeral recognition is one of the most popular fields of research in automation because it is used in many applications. Indeed, automation has continually received substantial attention from researchers. Therefore, great efforts have been made to devise accurate recognition methods with high recognition ratios. In this paper, we propose a method for integrating the correlation coefficient with a Self-Organizing Maps (SOM)-based technique to recognize offline handwritten Arabic decimal digits. The simulation results show very high recognition rates compared with the rates achieved by other existing methods.

Improvement of the quadratic sieve method on the basis of the extended factor base and using available quantity of B – smooth numbers

In information and telecommunication systems, RSA algorithms are often used to solve information security problems. At the core of the cryptostability of the most popular today asymmetric cryptographic algorithm RSA is the complexity of the factorization of large integers. Quadratic sieve method is the best for factorization of integers under 110 decimal digits or so. The most time consuming part of the algorithm of a quadratic sieve is the sieving process. The size of the factor base is one of the key parameters that determine the effectiveness of the sieving algorithm. Too large factor base requires the search for a large number of B–smooth numbers, which increases the total execution time of the algorithm. When the size is less than necessary, it will not be possible to find a sufficient number of B–smooth numbers. In this paper, the method for determining and applying a sufficient size of B–smooth numbers with doubling the factor base size in comparison with the basic algorithm of a quadratic sieve is proposed. With the expansion of the factor base, the number of N numbers increases, which can be decomposed into factors by the quadratic sieve method. It is also noted that its increase leads to an increase in computational complexity, since it is advisable to find a greater number of B–smooth numbers. However, when conducting numerical experiments, where the size of the factor base increased twice, it turned out that using the proposed algorithm, the time necessary to find a sufficient number of B-smooth numbers, on the contrary, decreased.

Rigorous effective bounds on the Hausdorff dimension of continued fraction Cantor sets: A hundred decimal digits for the dimension of E2

We prove that the algorithm of [19] for approximating the Hausdorff dimension of dynamically defined Cantor sets, using periodic points of the underlying dynamical system, can be used to establish completely rigorous high accuracy bounds on the dimension. The effectiveness of these rigorous estimates is illustrated for Cantor sets consisting of continued fraction expansions with restricted digits. For example the Hausdorff dimension of the set E2 (of those reals whose continued fraction expansion only contains digits 1 and 2) can be rigorously approximated, with an accuracy of over 100 decimal places, using points of period up to 25.The method for establishing rigorous dimension bounds involves the holomorphic extension of mappings associated to the allowed continued fraction digits, an appropriate disc which is contracted by these mappings, and an associated transfer operator acting on the Hilbert Hardy space of analytic functions on this disc. We introduce methods for rigorously bounding the approximation numbers for the transfer operators, showing that this leads to effective estimates on the Taylor coefficients of the associated determinant, and hence to explicit bounds on the Hausdorff dimension.

High Performance Parallel Decimal Multipliers Using Hybrid BCD Codes

A parallel decimal multiplier with improved performance is proposed in this paper by exploiting the properties of three different binary coded decimal (BCD) codes, namely the redundant BCD excess-3 code (XS-3), the overloaded decimal digit set (ODDS) code and the BCD-4221/5211 code. The signed-digit radix-10 recoding is used to recode the BCD multiplier to the digit set [-5, 5] from [0, 9]. The redundant BCD XS-3 code is adopted to generate the multiplicand multiples in a carry-free manner. The XS-3 coded partial products (PPs) are converted to ODDS PPs to fit binary partial product reduction (PPR). In this paper, a regular decimal PPR tree using ODDS and BCD-4221/5211 codes is proposed; it consists of a binary PPR tree block, a non-fixed size BCD-4221 counter block and a BCD-4221/5211 PPR tree block. The decimal carry-save algorithm based on BCD-4221/5211 is used in the PPR tree to obtain high performance multipliers. Moreover, an improved PPG circuit and an improved parallel prefix/carry-select decimal adder are proposed to further improve the performance of the proposed multipliers. Analysis and comparison using the 45 nm technology show that the proposed decimal multipliers are faster and require less hardware area than previous designs found in the technical literature.

Novel near-infrared spectrum analysis tool: Synergy adaptive moving window model based on immune clone algorithm

This paper presents a novel spectrum analysis tool named synergy adaptive moving window modeling based on immune clone algorithm (SA-MWM-ICA) considering the tedious and inconvenient labor involved in the selection of pre-processing methods and spectral variables by prior experience. In this work, immune clone algorithm is first introduced into the spectrum analysis field as a new optimization strategy, covering the shortage of the relative traditional methods. Based on the working principle of the human immune system, the performance of the quantitative model is regarded as antigen, and a special vector corresponding to the above mentioned antigen is regarded as antibody. The antibody contains a pre-processing method optimization region which is created by 11 decimal digits, and a spectrum variable optimization region which is formed by some moving windows with changeable width and position. A set of original antibodies are created by modeling with this algorithm. After calculating the affinity of these antibodies, those with high affinity will be selected to clone. The regulation for cloning is that the higher the affinity, the more copies will be. In the next step, another import operation named hyper-mutation is applied to the antibodies after cloning. Moreover, the regulation for hyper-mutation is that the lower the affinity, the more possibility will be. Several antibodies with high affinity will be created on the basis of these steps. Groups of simulated dataset, gasoline near-infrared spectra dataset, and soil near-infrared spectra dataset are employed to verify and illustrate the performance of SA-MWM-ICA. Analysis results show that the performance of the quantitative models adopted by SA-MWM-ICA are better especially for structures with relatively complex spectra than traditional models such as partial least squares (PLS), moving window PLS (MWPLS), genetic algorithm PLS (GAPLS), and pretreatment method classification and adjustable parameter changeable size moving window PLS (CA-CSMWPLS). The selected pre-processing methods and spectrum variables are easily explained. The proposed method will converge in few generations and can be used not only for near-infrared spectroscopy analysis but also for other similar spectral analysis, such as infrared spectroscopy.