Area-Optimized BCD-4221 VSLI Adder Architecture for High-Performance Computing

Decimal arithmetic circuits are promising to provide a solution for accurate decimal arithmetic operations which are not possible with binary arithmetic circuits.They can be used in banking,commercial and financial transactions,scientific measurements,etc.This article presents the Very Large Scale Integration(VLSI)design of Binary Coded Decimal(BCD)-4221 area-optimized adder architecture using unconventional BCD-4221 representation.Unconventional BCD number representations such as BCD4221 also possess the additional advantage of more effectively representing the 10's complement representation which can be used to accelerate the decimal arithmetic operations.The design uses a binary Carry Lookahead Adder(CLA)along with some other logic blocks which are required to perform internal calculations with BCD-4221 numbers.The design is verified by using Xilinx Vivado 2016.1.Synthesis results have been obtained by Cadence Genus16.1 synthesis tool using 90 nm technology.The performance parameters such as area,power,delay,and area-delay Product(ADP)are compared with earlier reported circuits.Our proposed circuit shows significant area and ADP improvement over existing designs.

Characteristics of Multi-Objective Linear Programming Problem and Multi-Objective Linear Fractional Programming Problem Taking Maximum Value of Multi-Objective Functions

In this paper, a new statistical averaging technique is proposed for finding an optimal solution to a multi-objective linear fractional programming problem (MOLFPP) and multi-objective linear programming problem (MOLPP) by using new arithmetic averaging method and new geometric averaging method. It is significantly noticeable same characteristics among all the technique while taking maximum or minimum among all optimized values for multi-objective functions using simplex algorithm. The characteristics provided from the problems are verified by the numerical examples.

ON THE LEAST PRIME IN AN ARITHMETICAL PROGRESSION(Ⅲ)

Let D be a large integer, and P（D,K） the least prime in the progression {Dn + K:n∈ N, 0【K≤D, （D,K） = 1}. In this paper, we shall prove P（D, K）? D13.5.

ON DISTRIBUTION OF PRIMES IN AN ARITHMETICAL PROGRESSION

Let x≥exp(exp(11 .5)) be a real number, a and q be positive integers satisfying (logx)3, (a,q) = 1. In this paper we prove0.13xq0.5(logx)-10.33, where denotes ,μ(n) denotes the Mobius function, ψ(x;q,l) (?)(n), and T(~X) = ~X(h)e(h/q). If there exists a real character ~X (mod q)such that L(~β,~X) = 0, ~β≥1-0.1077/logq, then ~E =1; otherwise ~E = 0.

Some Properties of Completely Arithmetical Rings

In this paper, we introduce the concept of completely arithmetical rings and investigate their properties. In particular, we prove that if R is a completely arithmetical ring with J（R） =0, then Ko（R） ≌Z^n for some positive integer n. We also show that such a ring is precisely a ring in which every proper ideal can be written uniquely as a product of finitely many distinct completely strongly irreducible ideals.

Integrated Analysis of Water Quality in Artificial Fishponds Using WQI and GIS in South-East Sierra Leone

Artificial fishponds play a pivotal role in global aquaculture, serving as a source of livelihood and nourishment for many communities. Ensuring the sustained health and productivity of Fishes in these environments relies heavily on water quality management. This assessment was done to determine the water quality of ten artificial fishponds in the south-eastern part of Sierra Leone using twelve physicochemical factors (pH, BOD, EC, TDS, turbidity, COD, Fe2+, Mg2+, Ca2+, NH3, , and alkalinity) to find out the Water Quality Index (WQI) and spatial distribution of respective parameters. The assessment of artificial fishponds using WQI and Inverse Distant Weighting (IDW) integration represents a relatively underexplored area within the domain of environmental water resources. The WQI was determined using the “Weighted Arithmetic Water Quality Index’’ method. The results of WQI in the study area range from 65.05 to 147.26. Several locations have water quality deemed unsuitable for consumption, while others range from good to very poor. It is essential to address and improve water quality in locations categorized as unsuitable for consumption and very poor to ensure safe and healthy water sources. It was also clear from the calculation that the smaller the mean concentration value of the pH as compared to the ideal value (7), the smaller the WQI value and the better the water quality. To keep the artificial fishpond water in good condition, mass domestic use should be controlled, and draining of surrounding organic matter should be stopped in ponds Bo_001, Kenema_001, and Kenema_002.

Differential Evolution with Arithmetic Optimization Algorithm Enabled Multi-Hop Routing Protocol

Wireless Sensor Networks(WSN)has evolved into a key technology for ubiquitous living and the domain of interest has remained active in research owing to its extensive range of applications.In spite of this,it is challenging to design energy-efficient WSN.The routing approaches are leveraged to reduce the utilization of energy and prolonging the lifespan of network.In order to solve the restricted energy problem,it is essential to reduce the energy utilization of data,transmitted from the routing protocol and improve network development.In this background,the current study proposes a novel Differential Evolution with Arithmetic Optimization Algorithm Enabled Multi-hop Routing Protocol(DEAOA-MHRP)for WSN.The aim of the proposed DEAOA-MHRP model is select the optimal routes to reach the destination in WSN.To accomplish this,DEAOA-MHRP model initially integrates the concepts of Different Evolution(DE)and Arithmetic Optimization Algorithms(AOA)to improve convergence rate and solution quality.Besides,the inclusion of DE in traditional AOA helps in overcoming local optima problems.In addition,the proposed DEAOA-MRP technique derives a fitness function comprising two input variables such as residual energy and distance.In order to ensure the energy efficient performance of DEAOA-MHRP model,a detailed comparative study was conducted and the results established its superior performance over recent approaches.

Solving Arithmetic Word Problems of Entailing Deep Implicit Relations by Qualia Syntax-Semantic Model

Solving arithmetic word problems that entail deep implicit relations is still a challenging problem.However,significant progress has been made in solving Arithmetic Word Problems(AWP)over the past six decades.This paper proposes to discover deep implicit relations by qualia inference to solve Arithmetic Word Problems entailing Deep Implicit Relations(DIR-AWP),such as entailing commonsense or subject-domain knowledge involved in the problem-solving process.This paper proposes to take three steps to solve DIR-AWPs,in which the first three steps are used to conduct the qualia inference process.The first step uses the prepared set of qualia-quantity models to identify qualia scenes from the explicit relations extracted by the Syntax-Semantic(S2)method from the given problem.The second step adds missing entities and deep implicit relations in order using the identified qualia scenes and the qualia-quantity models,respectively.The third step distills the relations for solving the given problem by pruning the spare branches of the qualia dependency graph of all the acquired relations.The research contributes to the field by presenting a comprehensive approach combining explicit and implicit knowledge to enhance reasoning abilities.The experimental results on Math23K demonstrate hat the proposed algorithm is superior to the baseline algorithms in solving AWPs requiring deep implicit relations.

Fin Field Effect Transistor with Active 4-Bit Arithmetic Operations in 22 nm Technology

A design of a high-speed multi-core processor with compact size is a trending approach in the Integrated Circuits(ICs)fabrication industries.Because whenever device size comes down into narrow,designers facing many power den-sity issues should be reduced by scaling threshold voltage and supply voltage.Initially,Complementary Metal Oxide Semiconductor(CMOS)technology sup-ports power saving up to 32 nm gate length,but further scaling causes short severe channel effects such as threshold voltage swing,mobility degradation,and more leakage power(less than 32)at gate length.Hence,it directly affects the arithmetic logic unit(ALU),which suffers a significant power density of the scaled multi-core architecture.Therefore,it losses reliability features to get overheating and increased temperature.This paper presents a novel power mini-mization technique for active 4-bit ALU operations using Fin Field Effect Tran-sistor(FinFET)at 22 nm technology.Based on this,a diode is directly connected to the load transistor,and it is active only at the saturation region as a function.Thereby,the access transistor can cutoff of the leakage current,and sleep transis-tors control theflow of leakage current corresponding to each instant ALU opera-tion.The combination of transistors(access and sleep)reduces the leakage current from micro to nano-ampere.Further,the power minimization is achieved by con-necting the number of transistors(6T and 10T)of the FinFET structure to ALU with 22 nm technology.For simulation concerns,a Tanner(T-Spice)with 22 nm technology implements the proposed design,which reduces threshold vol-tage swing,supply power,leakage current,gate length delay,etc.As a result,it is quite suitable for the ALU architecture of a high-speed multi-core processor.

Spatio-Temporal Context-Guided Algorithm for Lossless Point Cloud Geometry Compression

Point cloud compression is critical to deploy 3D representation of the physical world such as 3D immersive telepresence,autonomous driving,and cultural heritage preservation.However,point cloud data are distributed irregularly and discontinuously in spatial and temporal domains,where redundant unoccupied voxels and weak correlations in 3D space make achieving efficient compression a challenging problem.In this paper,we propose a spatio-temporal context-guided algorithm for lossless point cloud geometry compression.The proposed scheme starts with dividing the point cloud into sliced layers of unit thickness along the longest axis.Then,it introduces a prediction method where both intraframe and inter-frame point clouds are available,by determining correspondences between adjacent layers and estimating the shortest path using the travelling salesman algorithm.Finally,the few prediction residual is efficiently compressed with optimal context-guided and adaptive fastmode arithmetic coding techniques.Experiments prove that the proposed method can effectively achieve low bit rate lossless compression of point cloud geometric information,and is suitable for 3D point cloud compression applicable to various types of scenes.

A Study of Solar Rotation and Differential Rotation

The Sun has solar rotation;nevertheless, many evidences have suggested that different latitude of the Sun rotates in different speed, which is now known as differential rotation. This work calculates the solar rotation speeds near the equator and 30? in the northern hemisphere using Fixed-Point Arithmetic method. The calculated results show a greater speed at the equator than the speed at 30?, indicating that the speed decreases as the latitude becomes higher. .

Arithmetic Operations of Generalized Trapezoidal Picture Fuzzy Numbers by Vertex Method

In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.

Diophantine Quotients and Remainders with Applications to Fermat and Pythagorean Equations

Diophantine equations have always fascinated mathematicians about existence, finitude, and the calculation of possible solutions. Among these equations, one of them will be the object of our research. This is the Pythagoras’- Fermat’s equation defined as follows. (1) when , it is well known that this equation has an infinity of solutions but has none (non-trivial) when . We also know that the last result, named Fermat-Wiles theorem (or FLT) was obtained at great expense and its understanding remains out of reach even for a good fringe of professional mathematicians. The aim of this research is to set up new simple but effective tools in the treatment of Diophantine equations and that of Pythagoras-Fermat. The tools put forward in this research are the properties of the quotients and the Diophantine remainders which we define as follows. Let a non-trivial triplet () solution of Equation (1) such that . and are called the Diophantine quotients and remainders of solution . We compute the remainder and the quotient of b and c by a using the division algorithm. Hence, we have: and et with . We prove the following important results. if and only if and if and only if . Also, we deduce that or for any hypothetical solution . We illustrate these results by effectively computing the Diophantine quotients and remainders in the case of Pythagorean triplets using a Python program. In the end, we apply the previous properties to directly prove a partial result of FLT. .

A Numerical Method for Solving Ill-Conditioned Equation Systems Arising from Radial Basis Functions

Continuously differentiable radial basis functions (C∞-RBFs), while being theoretically exponentially convergent are considered impractical computationally because the coefficient matrices are full and can become very ill- conditioned. Similarly, the Hilbert and Vandermonde have full matrices and become ill-conditioned. The difference between a coefficient matrix generated by C∞-RBFs for partial differential or integral equations and Hilbert and Vandermonde systems is that C∞-RBFs are very sensitive to small changes in the adjustable parameters. These parameters affect the condition number and solution accuracy. The error terrain has many local and global maxima and minima. To find stable and accurate numerical solutions for full linear equation systems, this study proposes a hybrid combination of block Gaussian elimination (BGE) combined with arbitrary precision arithmetic (APA) to minimize the accumulation of rounding errors. In the future, this algorithm can execute faster using preconditioners and implemented on massively parallel computers.

Lanchester equation for cognitive domain using hesitant fuzzy linguistic terms sets

Intelligent wars can take place not only in the physical domain and information domain but also in the cognitive domain.The cognitive domain will become the key domain to win in the future intelligent war.A Lanchester equation considering cognitive domain is proposed to fit the development tendency intelligent wars in this paper.One party is considered to obtain the exponential enhancement advantage on combat forces in combat if it can gain an advantage in the cognitive domain over the other party according to the systemic advantage function.The operational effectiveness of the cognitive domain in war is considered to consist of a series of indicators.Hesitant fuzzy sets and linguistic term sets are powerful tools when evaluating indicators,hence the indicators are scored by experts using hesitant fuzzy linguistic terms sets here.A unique hesitant fuzzy hybrid arithmetical averaging operator is used to aggregate the evaluation.

Riemann Hypothesis, Catholic Information and Potential of Events with New Techniques for Financial and Other Applications

In this research we are going to define two new concepts: a) “The Potential of Events” (EP) and b) “The Catholic Information” (CI). The term CI derives from the ancient Greek language and declares all the Catholic (general) Logical Propositions () which will true for every element of a set A. We will study the Riemann Hypothesis in two stages: a) By using the EP we will prove that the distribution of events e (even) and o (odd) of Square Free Numbers (SFN) on the axis Ax(N) of naturals is Heads-Tails (H-T) type. b) By using the CI we will explain the way that the distribution of prime numbers can be correlated with the non-trivial zeros of the function ζ(s) of Riemann. The Introduction and the Chapter 2 are necessary for understanding the solution. In the Chapter 3 we will present a simple method of forecasting in many very useful applications (e.g. financial, technological, medical, social, etc) developing a generalization of this new, proven here, theory which we finally apply to the solution of RH. The following Introduction as well the Results with the Discussion at the end shed light about the possibility of the proof of all the above. The article consists of 9 chapters that are numbered by 1, 2, …, 9.

On modeling with multiplicative differential equations

This work is aimed to show that various problems from different fields can be modeled more efficiently using multiplicative calculus, in place of Newtonian calculus. Since multiplicative calculus is still in its infancy, some effort is put to explain its basic principles such as exponential arithmetic, multiplicative calculus, and multiplicative differential equations. Examples from finance, actuarial science, economics, and social sciences are presented with solutions using multiplicative calculus concepts. Based on the encouraging results obtained it is recommended that further research into this field be vested to exploit the applicability of multiplicative calculus in different fields as well as the development of multiplicative calculus concepts.

Reversible Natural Language Watermarking Using Synonym Substitution and Arithmetic Coding

For protecting the copyright of a text and recovering its original content harmlessly,this paper proposes a novel reversible natural language watermarking method that combines arithmetic coding and synonym substitution operations.By analyzing relative frequencies of synonymous words,synonyms employed for carrying payload are quantized into an unbalanced and redundant binary sequence.The quantized binary sequence is compressed by adaptive binary arithmetic coding losslessly to provide a spare for accommodating additional data.Then,the compressed data appended with the watermark are embedded into the cover text via synonym substitutions in an invertible manner.On the receiver side,the watermark and compressed data can be extracted by decoding the values of synonyms in the watermarked text,as a result of which the original context can be perfectly recovered by decompressing the extracted compressed data and substituting the replaced synonyms with their original synonyms.Experimental results demonstrate that the proposed method can extract the watermark successfully and achieve a lossless recovery of the original text.Additionally,it achieves a high embedding capacity.

Using LMS Adaptive Filter in Direct Wave Cancellation

The way to use the least-mean-square (LMS) arithmetic to cancel the direct wave for a passive radar system is introduced. The model of the direct wave is deduced. By using the LMS adaptive FIR filter, the software solution for FM passive radar system is developed instead of the hardware consumption of the existent experiment system of passive radar. Further more some simulative results are given. The simulative results indicate that using LMS arithmetic to cancel the direct wave is effective.