Search results for: elliptic curves

Authors: Abdelhakim Chillali, Abdelhamid Tadmori, Muhammed Ziane

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In this article we will study the elliptic curve defined over the ring An and we define the mathematical operations of ECC, which provides a high security and advantage for wireless applications compared to other asymmetric key cryptosystem.

Keywords: elliptic curves, finite ring, cryptography, study

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Authors: Siti Noor Farwina Anwar, Hailiza Kamarulhaili

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In this paper, we present the idea of implementing the Integer Sub-Decomposition (ISD) method on elliptic curves with j-invariant 1728. The ISD method was proposed in 2013 to compute scalar multiplication in elliptic curves, which remains to be the most expensive operation in Elliptic Curve Cryptography (ECC). However, the original ISD method only works on integer number field and solve integer scalar multiplication. By extending the method into the complex quadratic field, we are able to solve complex multiplication and implement the ISD method on elliptic curves with j-invariant 1728. The curve with j-invariant 1728 has a unique discriminant of the imaginary quadratic field. This unique discriminant of quadratic field yields a unique efficiently computable endomorphism, which later able to speed up the computations on this curve. However, the ISD method needs three endomorphisms to be accomplished. Hence, we choose all three endomorphisms to be from the same imaginary quadratic field as the curve itself, where the first endomorphism is the unique endomorphism yield from the discriminant of the imaginary quadratic field.

Keywords: efficiently computable endomorphism, elliptic scalar multiplication, j-invariant 1728, quadratic field

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Authors: Tun Myat Aung, Ni Ni Hla

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This paper begins by describing basic properties of finite field and elliptic curve cryptography over prime field and binary field. Then we discuss the discrete logarithm problem for elliptic curves and its properties. We study the general common attacks on elliptic curve discrete logarithm problem such as the Baby Step, Giant Step method, Pollard’s rho method and Pohlig-Hellman method, and describe in detail experiments of these attacks over prime field and binary field. The paper finishes by describing expected running time of the attacks and suggesting strong elliptic curves that are not susceptible to these attacks.c

Keywords: discrete logarithm problem, general attacks, elliptic curve, prime field, binary field

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Authors: G. Akgun, I. Algul, H. Kurtaran

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In this paper geometrically nonlinear static behavior of laminated composite hollow super-elliptic beams is investigated using generalized differential quadrature method. Super-elliptic beam can have both oval and elliptic cross-sections by adjusting parameters in super-ellipse formulation (also known as Lamé curves). Equilibrium equations of super-elliptic beam are obtained using the virtual work principle. Geometric nonlinearity is taken into account using von-Kármán nonlinear strain-displacement relations. Spatial derivatives in strains are expressed with the generalized differential quadrature method. Transverse shear effect is considered through the first-order shear deformation theory. Static equilibrium equations are solved using Newton-Raphson method. Several composite super-elliptic beam problems are solved with the proposed method. Effects of layer orientations of composite material, boundary conditions, ovality and ellipticity on bending behavior are investigated.

Keywords: generalized differential quadrature, geometric nonlinearity, laminated composite, super-elliptic cross-section

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Authors: Zhifu Li, Lei Li, Wanting Zhou, Yuanhang He

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This paper proposed a lightweight certificate-less authentication and key exchange protocol (Light-CL-PKC) based on elliptic curve cryptography and the Chinese Remainder Theorem for smart home scenarios. Light-CL-PKC can efficiently reduce the computational cost of both sides of authentication by forgoing time-consuming bilinear pair operations and making full use of point-addition and point-multiplication operations on elliptic curves. The authentication and key exchange processes in this system are also completed in a a single round of communication between the two parties. The analysis result demonstrates that it can significantly minimize the communication overhead of more than 32.14% compared with the referenced protocols, while the runtime for both authentication and key exchange have also been significantly reduced.

Keywords: authentication, key exchange, certificateless public key cryptography, elliptic curve cryptography

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Authors: Mustapha Benssalah, Mustapha Djeddou, Karim Drouiche

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The random number generation (RNG) presents a significant importance for the security and the privacy of numerous applications, such as RFID technology and smart cards. Since, the quality of the generated bit sequences is paramount that a weak internal generator for example, can directly cause the entire application to be insecure, and thus it makes no sense to employ strong algorithms for the application. In this paper, we propose a new pseudo random number generator (PRNG), suitable for cryptosystems ECC-based, constructed by randomly selecting points from several elliptic curves randomly selected. The main contribution of this work is the increasing of the generator internal states by extending the set of its output realizations to several curves auto-selected. The quality and the statistical characteristics of the proposed PRNG are validated using the Chi-square goodness of fit test and the empirical Special Publication 800-22 statistical test suite issued by NIST.

Keywords: PRNG, security, cryptosystem, ECC

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Authors: Edamana Krishnan, Khalil Al-Ghafri

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In this paper, modified K(n,n) and K(n+1,n+1) equations have been solved using mapping methods which give a variety of solutions in terms of Jacobi elliptic functions. The solutions when m approaches 0 and 1, with m as the modulus of the JEFs have also been deduced. The role of constraint conditions has been discussed.

Keywords: travelling wave solutions, solitary wave solutions, compactons, Jacobi elliptic functions, mapping methods

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Authors: Saif Akram, E. Rathakrishnan

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The mixing promoting efficiency of two identical sharp and truncated vertex triangular tabs offering geometrical blockage of 2.5% each, placed at the exit of a Mach 1.5 elliptic nozzle was studied experimentally. The effectiveness of both the tabs in enhancing the mixing of jets with the ambient air are determined by measuring the Pitot pressure along the jet axis and the jet spread in both the minor and major axes of the elliptic nozzle, covering marginally overexpanded to moderately underexpanded levels at the nozzle exit. The results reveal that both the tabs enhance mixing characteristics of the uncontrolled elliptic jet when placed at minor axis. A core length reduction of 67% is achieved at NPR 3 which is the overexpanded state. Similarly, the core length is reduced by about 67%, 50% and 57% at NPRs of 4, 5 and 6 (underexpanded states) respectively. However, unlike the considerable increment in mixing promoting efficiency by the use of truncated vertex tabs for axisymmetric jets, the effect is not much pronounced for the case of supersonic elliptic jets. The CPD plots for both the cases almost overlap, especially when tabs are placed at minor axis, at all the pressure conditions. While, when the tabs are used at major axis, in the case of overexpanded condition, the sharp vertex triangular tabs act as a better mixing enhancer for the supersonic elliptic jets. For the jet controlled with truncated vertex triangular tabs, the core length reductions are of the same order as those for the sharp vertex triangular tabs. The jet mixing is hardly influenced by the tip effect in case of supersonic elliptic jet.

Keywords: elliptic jet, tabs, truncated, triangular

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Authors: Lee Feng Koo, Tze Jin Wong, Pang Hung Yiu, Nik Mohd Asri Nik Long

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Greater common divisor (GCD) attack is an attack that relies on the polynomial structure of the cryptosystem. This attack required two plaintexts differ from a fixed number and encrypted under same modulus. This paper reports a security reaction of Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field under GCD attack. Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field was exposed mathematically to the GCD attack using GCD and Dickson polynomial. The result shows that the cryptanalyst is able to get the plaintext without decryption by using GCD attack. Thus, the study concluded that it is highly perilous when two plaintexts have a slight difference from a fixed number in the same Elliptic curve group over finite field.

Keywords: decryption, encryption, elliptic curve, greater common divisor

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Authors: Shiji Hu, Lei Li, Wanting Zhou, DaoHong Yang

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The data encryption, is the foundation of today’s communication. On this basis, how to improve the speed of data encryption and decryption is always a problem that scholars work for. In this paper, we proposed an elliptic curve crypto processor architecture based on SM2 prime field. In terms of hardware implementation, we optimized the algorithms in different stages of the structure. In finite field modulo operation, we proposed an optimized improvement of Karatsuba-Ofman multiplication algorithm, and shorten the critical path through pipeline structure in the algorithm implementation. Based on SM2 recommended prime field, a fast modular reduction algorithm is used to reduce 512-bit wide data obtained from the multiplication unit. The radix-4 extended Euclidean algorithm was used to realize the conversion between affine coordinate system and Jacobi projective coordinate system. In the parallel scheduling of point operations on elliptic curves, we proposed a three-level parallel structure of point addition and point double based on the Jacobian projective coordinate system. Combined with the scalar multiplication algorithm, we added mutual pre-operation to the point addition and double point operation to improve the efficiency of the scalar point multiplication. The proposed ECC hardware architecture was verified and implemented on Xilinx Virtex-7 and ZYNQ-7 platforms, and each 256-bit scalar multiplication operation took 0.275ms. The performance for handling scalar multiplication is 32 times that of CPU(dual-core ARM Cortex-A9).

Keywords: Elliptic curve cryptosystems, SM2, modular multiplication, point multiplication.

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Authors: Chao-Qing Dai

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In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation.

Keywords: discrete sine-Gordon equation, variable coefficient Jacobian elliptic function method, exact solutions, equation

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Authors: Zahid Ullah, Atlas Khan

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The presented research is dedicated to an extensive examination of the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. This study holds significance in unraveling the complexities inherent in these equations and understanding the smoothness of their solutions. The focus is on analyzing the regularity of results, aiming to contribute to the broader field of mathematical theory. By delving into the intricacies of extremely degenerate elliptic equations, the research seeks to advance our understanding beyond conventional analyses, addressing challenges posed by degeneracy and pushing the boundaries of classical analytical methods. The motivation for this exploration lies in the practical applicability of mathematical models, particularly in real-world scenarios where physical phenomena exhibit characteristics that challenge traditional mathematical modeling. The research aspires to fill gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations, ultimately contributing to both theoretical foundations and practical applications in diverse scientific fields.

Keywords: investigating smoothness, extremely degenerate elliptic equations, regularity properties, mathematical analysis, complexity solutions

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Authors: K. Sanjayani, C. Saraswathy, S. Sreenivasan, S. Sudhahar, D. Suganya, K. S. Neelukumari, N. Vijayarangan

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Double Base Number System (DBNS) is an imminent system of representing a number using two bases namely 2 and 3, which has its application in Elliptic Curve Cryptography (ECC) and Digital Signature Algorithm (DSA).The previous binary method representation included only base 2. DBNS uses an approximation algorithm namely, Greedy Algorithm. By using this algorithm, the number of digits required to represent a larger number is less when compared to the standard binary method that uses base 2 algorithms. Hence, the computational speed is increased and time being reduced. The standard binary method uses binary digits 0 and 1 to represent a number whereas the DBNS method uses binary digit 1 alone to represent any number (canonical form). The greedy algorithm uses two ways to represent the number, one is by using only the positive summands and the other is by using both positive and negative summands. In this paper, arithmetic operations are used for elliptic curve cryptography. Elliptic curve discrete logarithm problem is the foundation for most of the day to day elliptic curve cryptography. This appears to be a momentous hard slog compared to digital logarithm problem. In elliptic curve digital signature algorithm, the key generation requires 160 bit of data by usage of standard binary representation. Whereas, the number of bits required generating the key can be reduced with the help of double base number representation. In this paper, a new technique is proposed to generate key during encryption and extraction of key in decryption.

Keywords: cryptography, double base number system, elliptic curve cryptography, elliptic curve digital signature algorithm

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Authors: A. Andreasyan, C. Connors

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The Elliptic Curve Digital Signature algorithm-based X509v3 certificates are becoming more popular due to their short public and private key sizes. Moreover, these certificates can be stored in Internet of Things (IoT) devices, with limited resources, using less memory and transmitted in network security protocols, such as Internet Key Exchange (IKE), Transport Layer Security (TLS) and Secure Shell (SSH) with less bandwidth. The proposed method gives another advantage, in that it increases the performance of the above-mentioned protocols in terms of key exchange by saving one scalar multiplication operation.

Keywords: cryptography, elliptic curve digital signature algorithm, key exchange, network security protocol

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Authors: Kaoutar Lamrini Uahabi, Mohamed Atounti

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In the present work, we consider one category of curves denoted by L(p, k, r, n). These curves are continuous arcs which are trajectories of roots of the trinomial equation zn = αzk + (1 − α), where z is a complex number, n and k are two integers such that 1 ≤ k ≤ n − 1 and α is a real parameter greater than 1. Denoting by L the union of all trinomial curves L(p, k, r, n) and using the box counting dimension as fractal dimension, we will prove that the dimension of L is equal to 3/2.

Keywords: feasible angles, fractal dimension, Minkowski sausage, trinomial curves, trinomial equation

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Authors: Jorge L. Nisperuza, Wilson Sandoval, Edward. A. Gil, Johan A. Jimenez

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In orbital mechanics, an active research topic is the calculation of interplanetary trajectories efficient in terms of energy and time. In this sense, this work concerns the calculation of the orbital elements for sending interplanetary probes in the extrasolar system TRAPPIST-1. Specifically, using the mathematical expressions of the circular and elliptical trajectory parameters, expressions for the flight time and the orbital transfer rate increase between orbits, the orbital parameters and the graphs of the trajectories of Hohmann and Hohmann bi-elliptic for sending a probe from the innermost planet to all the other planets of the studied system, are obtained. The relationship between the orbital transfer rate increments and the relationship between the flight times for the two transfer types is found. The results show that, for all cases under consideration, the Hohmann transfer results to be the least energy and temporary cost, a result according to the theory associated with Hohmann and Hohmann bi-elliptic transfers. Saving in the increase of the speed reaches up to 87% was found, and it happens for the transference between the two innermost planets, whereas the time of flight increases by a factor of up to 6.6 if one makes use of the bi-elliptic transfer, this for the case of sending a probe from the innermost planet to the outermost.

Keywords: bi-elliptic Hohmann transfer, exoplanet, extrasolar system, Hohmann transfer, TRAPPIST-1

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Authors: Mohamad Khairi Ishak

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Conventional public key crypto systems such as RSA (Ron Rivest, Adi Shamir and Leonard Adleman), DSA (Digital Signature Algorithm), and Elgamal are no longer efficient to be implemented in the small, memory constrained devices. Elliptic Curve Cryptography (ECC), which allows smaller key length as compared to conventional public key crypto systems, has thus become a very attractive choice for many applications. This paper describes implementation of an elliptic curve cryptography (ECC) encryption engine on a FPGA. The system has been implemented in 2 different key sizes, which are 131 bits and 163 bits. Area and timing analysis are provided for both key sizes for comparison. The crypto system, which has been implemented on Altera’s EPF10K200SBC600-1, has a hardware size of 5945/9984 and 6913/9984 of logic cells for 131 bits implementation and 163 bits implementation respectively. The crypto system operates up to 43 MHz, and performs point multiplication operation in 11.3 ms for 131 bits implementation and 14.9 ms for 163 bits implementation. In terms of speed, our crypto system is about 8 times faster than the software implementation of the same system.

Keywords: elliptic curve cryptography, FPGA, key sizes, memory

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Authors: Chao-Qing Dai

Abstract:

Two families of exact travelling solutions for the discrete sine-Gordon equation are constructed based on the variable-coefficient Jacobian elliptic function method and different transformations. When the modulus of Jacobian elliptic function solutions tends to 1, soliton solutions can be obtained. Some soliton solutions degenerate into the known solutions in literatures. Moreover, dynamical properties of exact solutions are investigated. Our analysis and results may have potential values for certain applications in modern nonlinear science and textile engineering.

Keywords: exact solutions, variable-coefficient Jacobian elliptic function method, discrete sine-Gordon equation, dynamical behaviors

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Authors: A. Perdomo, J. R. Bacca, Q. E. Jabid

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In recent years, technological and investigative progress has been achieved in the area of monitoring of equipment and installation as a result of a deeper understanding of physical phenomenon associated with the non-destructive tests (NDT). The modal analysis proposes an efficient solution to determine the dispersion curves of an arbitrary waveguide cross-sectional. Dispersion curves are essential in the discontinuity localization based on guided waves. In this work, an isotropic hollow cylinder is dynamically analyzed in ANSYS to obtain resonant frequencies and mode shapes all of them associated with the dispersion curves. The numerical results provide the relation between frequency and wavelength which is the foundation of the dispersion curves. Results of the simulation process are validated with the software GUIGW.

Keywords: ansys APDL, dispersion curves, guide waves, modal analysis

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Authors: Zahid Ullah, Atlas Khan

Abstract:

This research endeavors to explore the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. These equations hold significance in understanding complex physical systems like porous media flow, with applications spanning various branches of mathematics. The focus is on unraveling and analyzing regularity results to gain insights into the smoothness of solutions for these highly degenerate equations. Elliptic equations, fundamental in expressing and understanding diverse physical phenomena through partial differential equations (PDEs), are particularly adept at modeling steady-state and equilibrium behaviors. However, within the realm of elliptic equations, the subset of extremely degenerate cases presents a level of complexity that challenges traditional analytical methods, necessitating a deeper exploration of mathematical theory. While elliptic equations are celebrated for their versatility in capturing smooth and continuous behaviors across different disciplines, the introduction of degeneracy adds a layer of intricacy. Extremely degenerate elliptic equations are characterized by coefficients approaching singular behavior, posing non-trivial challenges in establishing classical solutions. Still, the exploration of extremely degenerate cases remains uncharted territory, requiring a profound understanding of mathematical structures and their implications. The motivation behind this research lies in addressing gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations. The study of extreme degeneracy is prompted by its prevalence in real-world applications, where physical phenomena often exhibit characteristics defying conventional mathematical modeling. Whether examining porous media flow or highly anisotropic materials, comprehending the regularity of solutions becomes crucial. Through this research, the aim is to contribute not only to the theoretical foundations of mathematics but also to the practical applicability of mathematical models in diverse scientific fields.

Keywords: elliptic equations, extremely degenerate, regularity results, partial differential equations, mathematical modeling, porous media flow

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Authors: Eun-Jun Yoon

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Deniable authentication protocol is a new security authentication mechanism which can enable a receiver to identify the true source of a given message, but not to prove the identity of the sender to a third party. In 2013, Kar proposed a secure ID-based deniable authentication protocol whose security is based on computational infeasibility of solving Elliptic Curve Diffie-Hellman Problem (ECDHP). Kar claimed that the proposed protocol achieves properties of deniable authentication, mutual authentication, and message confidentiality. However, this paper points out that Kar's protocol still suffers from sender spoofing attack and message modification attack unlike its claims.

Keywords: deniable authentication, elliptic curve cryptography, Diffie-Hellman problem, cryptanalysis

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Authors: Noratiqah Mohd Ariff, Abdul Aziz Jemain, Mohd Aftar Abu Bakar

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The construction of Intensity-Duration-Frequency (IDF) curves is one of the most common and useful tools in order to design hydraulic structures and to provide a mathematical relationship between rainfall characteristics. IDF curves, especially those in Peninsular Malaysia, are often built using moving windows of rainfalls. However, these windows do not represent the actual rainfall events since the duration of rainfalls is usually prefixed. Hence, instead of using moving windows, this study aims to find regionalized distributions for IDF curves of extreme rainfalls based on storm events. Homogeneity test is performed on annual maximum of storm intensities to identify homogeneous regions of storms in Peninsular Malaysia. The L-moment method is then used to regionalized Generalized Extreme Value (GEV) distribution of these annual maximums and subsequently. IDF curves are constructed using the regional distributions. The differences between the IDF curves obtained and IDF curves found using at-site GEV distributions are observed through the computation of the coefficient of variation of root mean square error, mean percentage difference and the coefficient of determination. The small differences implied that the construction of IDF curves could be simplified by finding a general probability distribution of each region. This will also help in constructing IDF curves for sites with no rainfall station.

Keywords: IDF curves, L-moments, regionalization, storm events

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Authors: Jihad H. Asad

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An expression for the Green’s function (GF) of anisotropic face cantered cubic (IFCC) lattice is evaluated analytically and numerically for a single impurity problem. The density of states (DOS), phase shift and scattering cross section are expressed in terms of complete elliptic integrals of the first kind.

Keywords: lattice Green's function, elliptic integral, physics, cubic lattice

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Authors: Aigul Manapova

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We consider an optimal control problem in the higher coefficient of nonlinear equations with a divergent elliptic operator and unbounded nonlinearity, and the Dirichlet boundary condition. The conditions imposed on the coefficients of the state equation are assumed to hold only in a small neighborhood of the exact solution to the original problem. This assumption suggests that the state equation involves nonlinearities of unlimited growth and considerably expands the class of admissible functions as solutions of the state equation. We obtain formulas for the first partial derivatives of the objective functional with respect to the control functions. To calculate the gradients the numerical solutions of the state and adjoint problems are used. We also prove that the gradient of the cost function is Lipchitz continuous.

Keywords: cost functional, differentiability, divergent elliptic operator, optimal control, unbounded nonlinearity

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Authors: H. R. Khodaei, M. Moradi, A. H. Tajik

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The type of foundation commonly used today for berthing dolphins is a set of tubular steel piles with large diameters, which are known as monopiles. The design of these monopiles is based on the theories related with laterally loaded piles. One of the most common methods to analyze and design the piles subjected to lateral loads is the p-y curves. In the present study, centrifuge tests are conducted in order to obtain the p-y curves. Series of tests were designed in order to investigate the scaling laws in the centrifuge for monotonic loading. Also, two important parameters, the embedded depth L of the pile in the soil and free length e of the pile, as well as their ratios were studied via five experimental tests. Finally, the p-y curves of API are presented to be compared with the curves obtained from the tests so that the differences could be demonstrated. The results show that the p-y curves proposed by API highly overestimate the lateral load bearing capacity. It suggests that these curves need correction and modification for each site as the soil conditions change.

Keywords: centrifuge modeling, monopile, lateral loading, p-y curves

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Authors: Kanshio Richard Tyokyaa, Jagadish Singh

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In this paper, we examined the location and stability of Out-Of-Plane Equilibrium points in the elliptic restricted three-body problem of an infinitesimal body when both primaries are taken as oblate spheroids with oblateness up to zonal harmonic J₄. The positions of the Equilibrium points L₆,₇ and their stability depend on the oblateness of the primaries and the eccentricity of their orbits. We explored the problem numerically to show the effects of parameters involved in the position and stability of the Out-Of-Plane Equilibrium points for the systems: HD188753 and Gliese 667. It is found that their positions are affected by the oblateness of the primaries, eccentricity and the semi-major axis of the orbits, but its stability behavior remains unchanged and is unstable.

Keywords: out-of-plane, equilibrium points, stability, elliptic restricted three-body problem, oblateness, zonal harmonic

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Authors: D. M. S. Bandara, Yunqi Lei, Ye Luo

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Fingerprints are suitable as long-term markers of human identity since they provide detailed and unique individual features which are difficult to alter and durable over life time. In this paper, we propose an algorithm to encrypt and decrypt fingerprint images by using a specially designed Elliptic Curve Cryptography (ECC) procedure based on block ciphers. In addition, to increase the confusing effect of fingerprint encryption, we also utilize a chaotic-behaved method called Arnold Cat Map (ACM) for a 2D scrambling of pixel locations in our method. Experimental results are carried out with various types of efficiency and security analyses. As a result, we demonstrate that the proposed fingerprint encryption/decryption algorithm is advantageous in several different aspects including efficiency, security and flexibility. In particular, using this algorithm, we achieve a margin of about 0.1% in the test of Number of Pixel Changing Rate (NPCR) values comparing to the-state-of-the-art performances.

Keywords: arnold cat map, biometric encryption, block cipher, elliptic curve cryptography, fingerprint encryption, Koblitz’s encoding

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Authors: Safwan Mawlood Hussien

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Internet of Things (IoT) is a promising technology has received considerable attention in different fields such as health, industry, defence, and agro, etc. Due to the limitation capacity of computing, storage, and communication, IoT objects are more vulnerable to attacks. Many solutions have been proposed to solve security issues, such as key management using symmetric-key ciphers. This study provides a scalable group distribution key management based on ECcryptography; with less transmitted messages The method has been validated through simulations in OMNeT++.

Keywords: elliptic curves, Diffie–Hellman, discrete logarithm problem, secure key exchange, WSN security, IoT security, smart-agro

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Authors: Pedro Mauricio Acosta, Carlos Andrés Caro

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This research presents the regionalization of IDF curves for the department of Boyacá, Colombia, which comprises 16 towns, including the provincial capital, Tunja. For regionalization adjustment parameters (U and alpha) of the IDF curves stations referred to in the studied area were used. Similar regionalization is used by the interpolation of intensities. In the case of regionalization by parameters found by the construction of the curves intensity, duration and frequency estimation methods using ordinary moments and maximum likelihood. Regionalization and interpolation of data were performed with the assistance of Arcgis software. Within the development of the project the best choice to provide a level of reliability such as to determine which of the options and ways to regionalize is best sought. The resulting isolines maps were made in the case of regionalization intensities, each map is associated with a different return period and duration in order to build IDF curves in the studied area. In the case of the regionalization maps parameters associated with each parameter were performed last.

Keywords: intensity duration, frequency curves, regionalization, hydrology

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Authors: Encarnacion Alvarez, Noemı Hidalgo-Rebollo, Juan F. Munoz, Francisco J. Blanco-Encomienda

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Many companies use the technique named as acceptance sampling which consists on the inspection and decision making regarding products. According to the results derived from this method, the company takes the decision of acceptance or rejection of a product. The acceptance sampling can be applied to the technology management, since the acceptance sampling can be seen as a tool to improve the design planning, operation and control of technological products. The theoretical operating characteristic (OC) curves are widely used when dealing with acceptance sampling. In this paper, we carry out Monte Carlo simulation studies to compare numerically the empirical OC curves derived from the empirical results to the customary theoretical OC curves. We analyze various possible scenarios in such a way that the differences between the empirical and theoretical curves can be observed under different situations.

Keywords: single-sampling plan, lot, Monte Carlo simulation, quality control

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