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This paper presents a comparative study of the performances of arithmetic units, based on different number systems like Residue Number System (RNS), Double Base Number System (DBNS), Triple Base Number System (TBNS) and Mixed Number System (MNS) for DSP applications. The performance analysis is carried out in terms of the hardware utilization, timing complexity and efficiency. The arithmetic units based on these number systems were employed in designing various modulation schemes like Binary Frequency Shift Keying (BFSK) modulator/demodulator. The analysis of the performance of the proposed modulator on above mentioned number systems indicates the superiority of other number systems over binary number system.

We announce the release of chromEvol version 2.0, a software tool for inferring the pattern of chromosome number change along a phylogeny. The software facilitates the inference of the expected number of polyploidy and dysploidy transitions along each branch of a phylogeny and estimates ancestral chromosome numbers at internal nodes. The new version features a novel extension of the model accounting for general multiplication events, other than doubling of the number of chromosomes. This allows the monoploid number (commonly referred to as x, or the base-number) of a group of interest to be inferred in a statistical framework. In addition, we devise an inference scheme, which allows explicit categorization of each terminal taxon as either diploid or polyploid. The new version also supports intraspecific variation in chromosome number and allows hypothesis testing regarding the root chromosome number. The software, alongside a detailed usage manual, is available at http://www.tau.ac.il/∼itaymay/cp/chromEvol/.

Interactive Conceptual Learning (ILC) based Multimedia has been developed to represent base of number concept turn into more interactive and meaningful learning. The first design of ILC based multimedia is multimedia supported computer that explore base of number concept in existing conceptual. Pre-service elementary teachers should be provided with the learning that can optimize the base of number conceptions. To collect and analyse data comprehensively, researchers developed a 3D-1I developing method which has comprehensive stages: analysis, design, development, implementation and evaluation. The 3D-1I developing stage has been utilized to describe comprehensively ILC based Multimedia. It can be proved with the increasing average score from 30.10 on pretest to 82.33 on posttest of pre service teachers’ understanding on base number concept. Based on data analysis, it can be concluded that ILC-based multimedia could effectively improve pre-service teachers’ conceptual understanding on base of number concept.

DNA is believed to be a promising candidate for molecular logic computation, and the fluorogenic/colorimetric substrates of G-quadruplex DNAzyme (G4zyme) are broadly used as label-free output reporters of DNA logic circuits. Herein, for the first time, tyramine-HCl (a fluorogenic substrate of G4zyme) is applied to DNA logic computation and a series of label-free DNA-input logic gates, including elementary AND, OR, and INHIBIT logic gates, as well as a two to one encoder, are constructed. Furthermore, a DNA caliper that can measure the base number of target DNA as low as three bases is also fabricated. This DNA caliper can also perform concatenated AND-AND logic computation to fulfil the requirements of sophisticated logic computing.

Because of the rapid increasing of malware, one of the main challenges in malware detection is how to do malware classification automatically. Although there are many automatic classification methods recently, their results still get high false positive rate. Since the base number of malware samples is huge, a very small false positive can cause a big number of false alarms. Essentially, high false positive rate is usually caused by the adoption of obfuscation and evasion technology by malware. As a result, one or more features would be disguised. In this paper, we propose one method using multi-features to mitigate the effect of disguised features. Through this method, each kind of features is extracted independently, and used to train one classifier respectively. The system adopts the prediction if and only if the output of each classifier is the same. To test our method, we use both static and dynamic features to classify 282 samples. The experiment result shows that this method could improve the accuracy of malware classification and achieve nearly no false positive.

We introduce here a generalized method a new Algorithm to find Triple-Base number system and Triple-Base chain and hence in turn Single Digit Triple-Base number system(SDTBNS). The proposed method is not only simpler and faster than the Algorithms to find Double-Base number system or Double-Base chain, experimentally it also returns a shorter length of Triple-Base chain which in turn reduces the size of the look-up-table to find out SDTBNS. The complexity analysis and experimental results shows the novelty of the proposed Algorithm. Moreover when the proposed method is applied to find scalar multiplication in case of Elliptic Curve Cryptography and coefficient multiplication in case of designing digital filter, its efficiency also proves its novelty. Here we have used third base as 5 because when it is multiplied by 2 gives 10 which can be efficiently used for decimal shifting, i.e. if an integer 'n' can be represented in SDTBNS form, then n/10 x or nx10 x can also represented in SDTBNS only by diving or multiplying 'n' by 10.

International audience; Number systems with a rational number $a/b > 1$ as base have gained interest in recent years. In particular, relations to Mahler's $3/2$-problem as well as the Josephus problem have been established. In the present paper we show that the patterns of digits in the representations of positive integers in such a number system are uniformly distributed. We study the sum-of-digits function of number systems with rational base $a/b$ and use representations w.r.t. this base to construct normal numbers in base $a$ in the spirit of Champernowne. The main challenge in our proofs comes from the fact that the language of the representations of integers in these number systems is not context-free. The intricacy of this language makes it impossible to prove our results along classical lines. In particular, we use self-affine tiles that are defined in certain subrings of the adéle ring $\mathbb{A}_\mathbb{Q}$ and Fourier analysis in $\mathbb{A}_\mathbb{Q}$. With help of these tools we are able to reformulate our results as estimation problems for character sums.

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Chromosome number determinations are reported for 22 species of Australian Restionaceae. The segregation of new species formerly included in Lepyrodia scariosa R.Br. sens. lat. has required the redetermination of voucher specimens and some previously reported counts apply to the newly segregated species. A recent DNA-based phylogeny is a basis for discussing these findings together with previously reported counts. In Restionaceae n = 12 appears plesiomorphic in Leptocarpoideae, while both n = 7 and n = 9 are found in Sporadanthoideae.

In this paper, a new number system “Single Digit Triple Base Number System (SDTBNS)” using 2, 3 and 5 as the bases have been introduced. Advantages of SDTBNS over Single Digit Double Base Number System (SDDBNS) have been discussed here. Dynamic range of the numbers represented in SDTBNS has also been dealt with in details. Analysis on complexity of the multiplication unit and execution time reveal the novelty of the proposed number system. Application of this number system in digital signal processing(DSP) has been explored and an efficient implementation of linear convolution has been presented.

Execution of arithmetic operations at very high speed in real time is the major concern in digital signal processing (DSP) because DSP algorithms are computation intensive. In recent times, Residue Number Systems (RNS) are considered as alternative to binary number system because of their capabilities of performing "carry-free" addition and Multiplication. Double Base Number Systems (DBNS), another non-binary number systems are also increasingly becoming attractive for signal processing applications due to their capabilities of handling arithmetic operations, particularly multiplication efficiently. However, the complexity involved in converting binary to DBNS becomes a major bottleneck and the efficiency of performance decreases considerably due to large conversion time. So RNS Adder and DBNS Multiplier can be used to implement multiply & accumulate (MAC) units. Because RNS adders are less complex and faster compared to DBNS and DBNS multipliers are efficient compared to RNS multiplier. MAC units are the key units in Digital Signal Processors. In this paper we have shown how FIR filter can be implemented using the proposed "Mixed Number System MAC units".

Compute intensive signal Processing Algorithms demand efficient execution of high performance arithmetic operations. Since, double base number system (DBNS) offers high performance arithmetic units, it is gaining attention to many researchers .However, the advantage of DBNS can not be exploited due to large conversion time from binary to DBNS. Keeping this issue in view, this paper presents a novel conversion scheme using parallel search technique.

Non-binary number systems are increasingly gaining popularity in signal processing applications for their capabilities of handling arithmetic operations efficiently. One such number system, "Double Base Number System (DBNS)" has gained attention to many researchers for it's capability of performing multiplication operation efficiently. Recently, "Triple Base Number System (TBNS)" has been introduced which shows better performance over DBNS for higher bit operations in terms of speed, hardware complexity and power dissipation. However, the advantages of TBNS systems cannot be exploited due to substantial overhead of conversion from binary to TBNS. Keeping this issue in view, in this paper, a novel architecture has been proposed for high performance binary to TBNS conversion. Efficiency of this conversion scheme has been dealt with in details and experimental results and analysis clearly indicate the novelty of the architecture.

LETTER

This paper deals with rational base number systems for p-adic numbers. We mainly focus on the system proposed by Akiyama et al. in 2008, but we also show that this system is in some sense isomorphic to some other rational base number systems by means of finite transducers. We identify the numbers with finite and eventually periodic representations and we also determine the number of repre- sentations of a given p-adic number. Mathematics Subject Classification. 11A67, 11E95.

Number Theory and Cryptography are based on mathematical problems that are considered difficult to solve. “Difficult” in this case refers more to the computational requirements in finding a solution than to the conception of the problem. These problems are formally called “hard” problems. Some of the most well known examples are factoring large numbers, finding the discrete logarithms, theorem-proving, and the Traveling Salesman Problem. In the theory of Double Base Number System (DBNS)/Multiple Base Number System (MBNS), finding the best approximation for a given integer is a hard problem. This approximation can be used to compute Elliptic curve scalar multiplication in an efficient way. In this paper, we have come up with an algorithm for DBNS, which expresses any integer n in the form of DBNS with decreasing order of exponents.

The works of Erdos et al. about expansions of 1 with respect to a non-integer base q, referred to as q-expansions, are investigated to determine how far they continue to hold when the number 1 is replaced by a positive number x. It is found that most results about q-expansions for real numbers greater than or equal to 1 are in somewhat opposite direction to those for real numbers less than or equal to 1. The situation when a real number has a unique q-expansion, and when it has exactly two q-expansions are studied. The smallest base number q yielding a unique q-expansion is determined and a particular sequence is shown, in certain sense, to be the smallest sequence whose corresponding base number q yields exactly two q-expansions.

Double base number systems are increasingly attractive for many compute intensive applications especially in signal processing because of their capabilities of handling arithmetic operations efficiently. However, the complexity involved in converting binary to DBNS becomes a major bottleneck and the efficiency of performance goes down drastically due to the complexity involved in conversion . Since complexity of multi digit DBNS multiplications and additions increases with the number of digits ( index i ,j) ,in this paper a novel conversion scheme has been proposed where a given binary number will be converted to a single digit (index i ,j) double base number . The proposed scheme not only reduces the hardware complexity of the arithmetic operations but also reduces the time of execution.

In the paper, an algorithm called a Constraint algorithm is proposed to solve the fan-in problem occurred in ADC encoding circuits. The Flash ADC architecture uses a double-base number system (DBNS). The DBNS has known to represent the multi-dimensional logarithmic number system (MDLNS) used for implementing the multiplier accumulator architecture of FIR filter in digital signal processing (DSP) applications. The authors use the DBNS with the base 2 and 3 to represent binary output of ADC. A symmetric map is analyzed first, and then asymmetric map is followed to provide addition read DBNS to DSP circuitry. The simulation results are shown for the Double-Base Integer Encoder (DBIE) of the 6-bit ADC to demonstrate an effectiveness of the Constraint algorithm, using 0.18㎛ CMOS technology. The DBIE's processing speed of the ADC is fast compared to the FAT tree encoder circuit by 0.95 ㎓.

A new method for representing positive integers and real numbers in a rational base is considered. It amounts to computing the digits from right to left, least significant first. Every integer has a unique expansion. The set of expansions of the integers is not a regular language but nevertheless addition can be performed by a letter-to-letter finite right transducer. Every real number has at least one such expansion and a countable infinite number of them have more than one. We explain how these expansions can be approximated and characterize the expansions of reals that have two expansions. The results that we derive are pertinent on their own and also as they relate to other problems in combinatorics and number theory. A first example is a new interpretation and expansion of the constant K(p) from the so-called “Josephus problem.” More important, these expansions in the base p a llow us to make some progress in the problem of the distribution of the fractional part of the powers of rational numbers.

13 páginas., Chromosomal analyses were conducted for the first time in all three species of the Chilean endemic Epipetrum Phil. (Dioscoreaceae; the yam family). Mitotic chromosome counts showed that all studied individuals of the rare Epipetrum bilobum and E. polyanthes, and most studied individuals of the more widespread E. humile, had 2n = 14 chromosomes. However, two populations of E. humile had 2n = 28 chromosomes. The ideograms shared a similar karyotype constitution for the three species but with a duplicated chromosome number in some populations of E. humile. Our results suggest that the Epipetrum taxa are mainly diploids, with a base number of x = 7, and the tetraploid cytotypes have arisen only in few cases. After that of Borderea (x = 6), this chromosome base number is the second lowest one found in the Dioscoreaceae. Epipetrum and Borderea are two small, relict, satellite genera of the Dioscoreaceae, endemic to Chile (South America) and the Pyrenees (Southwestern Europe), respectively. The two taxa share several morphological attributes and are adapted to rocky and mountain habitats. However, whereas Borderea is an allotetra-ploid genus of relatively recent hybrid origin, Epipetrum is diploid in common with the species found in the early branching clades of Dioscorea.

In Signal Processing and Cryptography a non-standard number representation, called Double Base Number System (DBNS) has found many applications. This representation has many interesting and useful properties. In traditional number systems, there is one radix used to represent numbers. For example in decimal systems, numbers are expressed as sum of powers of 10. In DBNS numbers are represented as sum of product of powers of 2 radices. In the current article we present a scheme to represent numbers in double (and multi-) base format by combinatorial objects like graphs and diagraphs. The combinatorial representation leads to proof of some interesting results about the double and multibase representation of integers. These proofs are based on simple combinatorial arguments. In this article we have provided a graph theoretic proof of the recurrence relation satisfied by the number of double base representations of a given integer. The result has been further generalized to more than 2 bases. Also, we have uncovered some interesting properties of the sequence representing the number of double (multi-) base representation of a positive integer $n$. It is expected that the combinatorial representation can serve as a tool for a better understanding of the double (and multi-) base number systems and uncover some of the mysteries still associated with it.

Migration of fines, and formation of oil emulsion have been independently observed during smart water flooding both have been suggested to play a vital role in enhanced oil recovery (EOR). But, the exact role of fines and the reason of emulsion formation are not well studied for carbonate reservoirs. This study shows that addition of water and crude oil on calcite fines leads to formation of soluble oil emulsions in the water phase. Formation of these emulsions and its implication in EOR has been experimentally analyzed. To characterize the formation of theses emulsions study has been conducted for various water insoluble salts were used as fines (including, Li2CO3, MgCO3, CaCO3, CaSO4, SrSO4, BaSO4 and reservoir CaCO3 fines). Different types of oil and water was added to these fines. To study conditions of oil emulsion formation, design oil was used consisting of hexane and hexadecane. Heptylamine and hexadecylamine were doped in various compositions to mimic the base number of the oil. Experiments were conducted for pure crude oil and doped oil to understand its implications in EOR. Composition of initial and final floating oil was obtained through gas chromatographic (GC) analysis. The two were thereafter compared to obtain the composition of micelles formed. The experiments showed how oil emulsions were formed when polar hydrocarbons are present in the oil. Mixtures of alkanes did not produce emulsions. In oil containing hexadecylamine 95% of the initial hexadecylamine was accumulated in the emulsions and only 5% was found in the floating oil. In oil samples containing heptylamine only 45-50% of its initial amount was accumulated in the emulsions. This indicates heavier amines can form more stable emulsions. Oil emulsions were produced with all the fines used, but the composition of these emulsions were dependent on the salt anions. In all carbonates, lighter amines preferred emulsions formation with lighter alkane. No such selectivity was observed in any of the sulfates. Results obtained with crude, doped and designed oil were consistent for both pure salts and outcrops. These results show that fines of carbonate released during fracturing, or sulfates formed during smart water flooding can form mixed wet water soluble oil emulsions which help to mobilize trapped oil, and increase the sweep efficiency. The results clearly show oils with the same base number can have significantly different amount of emulsion formation with fines, and provides a detailed mechanism of further characterization of the oil. The study highlights the significance of fines during smart water flooding in carbonate reservoirs and shows how its role in EOR can be mistakenly underestimated.

This brief revisits the problem of conversion between number systems and asks the following question: given a nonnegative decimal number d, what is the value of the digit at position j in the corresponding base b number? Thus, we do not require the knowledge of other digits except the one we are interested in. Accordingly, we present a conversion function that relates each digit in a base b system to the decimal value that is equal to the base b number in question. We also show some applications of this new algorithm in the areas of parallel computing and cryptography

This paper explains about the power quality and transmits maximum power between the grid based electrical systems. These system stream calculations are connected to a graphical portrayal of a power framework topology to decide the base number of framework branches should have been lost keeping in mind the end goal to ensure separating the two hubs in the framework that are chosen. The number of framework branches that are discovered fills in as an inexact marker of framework vulnerabilities. The technique utilized as a part of these availability investigations makes utilization of surely understood diagram hypothesis organize stream greatest stream calculations, additionally presents another calculation for refreshing an old system stream answer for the misfortune of just a solitary framework branch. The proposed new calculation permits for essentially diminished arrangement time that is fancied in a ongoing condition. The benefit of utilizing the proposed technique is delineated by utilizing a point by point case of the 2008 island development that happened in the Entergy control framework.

Development of the era had a considerable impact on the existence of a language. To overcome this there are some efforts to be made, one of which is to create a dictionary, a dictionary that was made to be practical and quick in use. Dictionary in question is a dictionary based on Android. To create a dictionary-based android can use string matching algorithm, one of the string matching algorithm is the Rabin-Karp algorithm, Rabin-Karp algorithm perform string matching hash value based on the text and the pattern hash value. The study produced an android based dictionary application which the base number is used to generate a hash value greatly affects the speed of search words. Average running time of 10 attempts to search for words is 14.9 ms.

In this paper, we analyze some of the main properties of a double base number system, using bases 2 and 3; in particular, we emphasize the sparseness of the representation. A simple geometric interpretation allows an efficient implementation of the basic arithmetic operations and we introduce an index calculus for logarithmic-like arithmetic with considerable hardware reductions in lookup table size. We discuss the application of this number system in the area of digital signal processing; we illustrate the discussion with examples of finite impulse response filtering.

In a review of chromosome numbers in the genus Potamogeton, we highlight numerous errors that have crept into the literature. These have resulted chiefly from reliance on abstracts in chromosome number indices and compilations, rather than on the original publications, but partly also because of misleading summaries even in the primary literature. We present a list of counts that we believe are original and genuine, and a list of those that were never made but which nevertheless appear in the literature. Scrutiny of the list of accepted counts indicates that aneuploidy is widespread in the genus and that transition between the two common chromosome numbers (2n=26 and 2n=28) has occurred several times. Currently available data are insufficient to resolve the question of the ancestral base number. We also present details of the first chromosome counts from English populations of five taxa: P. polygonifolius Pourr. (2n=28), P. pectinatus L. (2n=ca. 78), P. perfoliatus L. (2n=ca. 52), P.×nitens Weber (P. gramineus×P. perfoliatus) (2n=ca. 52) and P.×salicifolius Wolfg. (P. lucens×P. perfoliatus) (2n=ca. 52).

ポリエステル系ポリマー塗料用樹脂の水酸基価と酸価の同時定量を目的として,近赤外透過スペクトル測定と多変量解析を行った.試料ごとのバックグラウンドの違いを補正するために,拡散透過の理論式から試料固有の吸収係数スペクトルを推定し,PLSl (partial lcast squares)法を適用した.提案手法の定量精度にはまだ改善の余地があるが,簡便な水酸基価と酸価の同時定量法として使用できることを確認した.