• Journal of the Korean Data and Information Science Society
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• 제14권2호
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• pp.385-391
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• 2003

A sequence of n Bernoulli trials which violates the constant success probability assumption is termed as "Poisson trials". In this paper, the recurrence formula for the r-th central moment of number of successes with n Poisson trials is derived. Romanovsky's method, based on the differentiation of characteristic function, is used in the derivation of recurrence formula for the central moments of conventional binomial distribution. Romanovsky's method is applied to that of Poisson trials in this paper. Some central moment calculation results are given to compare the central moments of Poisson trials with those of conventional binomial distribution.

• Coupled systems mechanics
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• 제5권2호
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• pp.157-190
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• 2016

This paper deals with frequency analysis of Euler-Bernoulli beams carrying an arbitrary number of Kelvin-Voigt viscoelastic dampers, subjected to harmonic loads. Multiple external/internal dampers occurring at the same position along the beam axis, modeling external damping devices and internal damping due to damage or imperfect connections, are considered. The challenge is to handle simultaneous discontinuities of the response, in particular bending-moment/rotation discontinuities at the location of external/internal rotational dampers, shear-force/deflection discontinuities at the location of external/internal translational dampers. Following a generalized function approach, the paper will show that exact closed-form expressions of the frequency response under point/polynomial loads can readily be derived, for any number of dampers. Also, the exact dynamic stiffness matrix and load vector of the beam will be built in a closed analytical form, to be used in a standard assemblage procedure for exact frequency response analysis of frames.

• 한국음향학회지
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• 제19권8호
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• pp.3-11
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• 2000

음성의 특성은 지연에 매우 민감한 (delay-sensitive) 트래픽으로 시스템에서 손실에 민감한 (loss-sensitive) 다른 트래픽과 동일한 방식으로 서비스되어서는 두 트래픽 모두의 QoS (Quality of Service)를 만족시킬 수 없다. 효율적인 트래픽의 처리를 위해서는 시스템의 상태에 따라 손실에 민감한 트래픽에 영향을 적게 주면서 지연민감 트래픽의 성능도 만족하는 것이 바람직하다. 본 논문에서 도입한 동적우선권제어함수 (Dynamic Priority Control Function, DPCF)는 시스템의 상태에 따라 각 트래픽에 우선권을 동적으로 할당하여 서비스 스케줄링을 제어하는 함수f(·)로 기존의 우선권 제어방식을 더욱 일반화시킨 방식이다. 클래스 1의 손실민감 트래픽과 음성과 같은 클래스 2의 지연민감 트래픽을 수용하는 시스템에 TBPJ (Threshold-based Bernoulli Priority Jump) 방식의 DPCF을 적용하여 성능을 분석하였다. DPCF은 각 시스템에 대기하고 있는 트래픽의 양과 시스템의 가용 용량인 버퍼의 threshold에 따라 각 트래픽 클래스에 우선권을 동적으로 할당하여 서비스가 이루어지도록 한다. 성능분석을 통하여 TBPJ 제어방식이 기존의 우선권 제어 방식보다 성능 및 효율성에 있어서 우수함을 입증하였다. 즉 성능을 분석한 결과 손실민감 트래픽의 성능저하는 미미하고 지연민감 트래픽의 성능향상은 현저히 개선된 것을 확인하였다.

• Smart Structures and Systems
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• 제12권5호
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• pp.501-521
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• 2013

This paper is concerned with static and dynamic shape control of a laminated Bernoulli-Euler beam hosting a uniformly distributed array of resistively interconnected piezoelectric patches. We present an analytical one-dimensional model for a laminated piezoelectric beam with material discontinuities within the framework of Bernoulli-Euler and extent the model by a network of resistors which are connected to several piezoelectric patch actuators. The voltage of only one piezoelectric patch is prescribed: we answer the question how to design the interconnected resistive electric network in order to annihilate lateral vibrations of a cantilever. As a practical example, a cantilever with eight patch actuators under the influence of a tip-force is studied. It is found that the deflection at eight arbitrary points along the beam axis may be controlled independently, if the local action of the piezoelectric patches is equal in magnitude, but opposite in sign, to the external load. This is achieved by the proper design of the resistive network and a suitable choice of the input voltage signal. The validity of our method is exact in the static case for a Bernoulli-Euler beam, but it also gives satisfactory results at higher frequencies and for transient excitations. As long as a certain non-dimensional parameter, involving the number of the piezoelectric patches, the sum of the resistances in the electric network and the excitation frequency, is small, the proposed shape control method is approximately fulfilled for dynamic load excitations. We evaluate the feasibility of the proposed shape control method with a more refined model, by comparing the results of our one-dimensional calculations based on the extended Bernoulli-Euler equations to three-dimensional electromechanically coupled finite element results in ANSYS 12.0. The results with the simple Bernoulli-Euler model agree well with the three-dimensional finite element results.

• Structural Engineering and Mechanics
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• 제53권3호
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• pp.537-573
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• 2015

Multiple-step beams carrying intermediate lumped masses with/without rotary inertias are widely used in engineering applications, but in the literature for free vibration analysis of such structural systems; Bernoulli-Euler Beam Theory (BEBT) without axial force effect is used. The literature regarding the free vibration analysis of Bernoulli-Euler single-span beams carrying a number of spring-mass systems, Bernoulli-Euler multiple-step and multi-span beams carrying multiple spring-mass systems and multiple point masses are plenty, but that of Timoshenko multiple-step beams carrying intermediate lumped masses and/or rotary inertias with axial force effect is fewer. The purpose of this paper is to utilize Numerical Assembly Technique (NAT) and Differential Transform Method (DTM) to determine the exact natural frequencies and mode shapes of the axial-loaded Timoshenko multiple-step beam carrying a number of intermediate lumped masses and/or rotary inertias. The model allows analyzing the influence of the shear and axial force effects, intermediate lumped masses and rotary inertias on the free vibration analysis of the multiple-step beams by using Timoshenko Beam Theory (TBT). At first, the coefficient matrices for the intermediate lumped mass with rotary inertia, the step change in cross-section, left-end support and right-end support of the multiple-step Timoshenko beam are derived from the analytical solution. After the derivation of the coefficient matrices, NAT is used to establish the overall coefficient matrix for the whole vibrating system. Finally, equating the overall coefficient matrix to zero one determines the natural frequencies of the vibrating system and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the differential equations of the motion. The calculated natural frequencies of Timoshenko multiple-step beam carrying intermediate lumped masses and/or rotary inertias for the different values of axial force are given in tables. The first five mode shapes are presented in graphs. The effects of axial force, intermediate lumped masses and rotary inertias on the free vibration analysis of Timoshenko multiple-step beam are investigated.

• 대한수학회보
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• 제60권4호
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• pp.933-955
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• 2023

For any prime number p, let J(p) be the set of positive integers n such that the numerator of the n^th harmonic number in the lowest terms is divisible by this prime number p. We consider an extension of this set to the generalized harmonic numbers, which are a natural extension of the harmonic numbers. Then, we present an upper bound for the number of elements in this set. Moreover, we state an explicit condition to show the finiteness of our set, together with relations to Bernoulli and Euler numbers.

• International Journal of Computer Science & Network Security
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• 제21권2호
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• pp.229-237
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• 2021

Our modern 'information-hungry' age demands delivery of information at unprecedented fast rates. Timely delivery of noteworthy information about recent events can help people from different segments of life in number of ways. As world has become global village, the flow of news in terms of volume and speed demands involvement of machines to help humans to handle the enormous data. News are presented to public in forms of video, audio, image and text. News text available on internet is a source of knowledge for billions of internet users. Urdu language is spoken and understood by millions of people from Indian subcontinent. Availability of online Urdu news enable this branch of humanity to improve their understandings of the world and make their decisions. This paper uses available online Urdu news data to train machines to automatically categorize provided news. Various machine learning algorithms were used on news headline for training purpose and the results demonstrate that Bernoulli Naïve Bayes (Bernoulli NB) and Multinomial Naïve Bayes (Multinomial NB) algorithm outperformed other algorithms in terms of all performance parameters. The maximum level of accuracy achieved for the dataset was 94.278% by multinomial NB classifier followed by Bernoulli NB classifier with accuracy of 94.274% when Urdu stop words were removed from dataset. The results suggest that short text of headlines of news can be used as an input for text categorization process.

• 한국정보처리학회논문지
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• 제7권11S호
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• pp.3684-3693
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• 2000

본 논문에서는 다양한 트래픽을 수용해야 하는 차세대 인터넷에서 핵심적인 기능을 담당하는 고속 패킷스위치를 위한 동적우선권제어함수(Dynamic Priority Control Function)이 개념을 도입하고 TBPJ(Threshold-based Bernoulli Priority Jump) 방식에 대한 성능분석을 하였다. 동적우선권제어함수(Dynamic Priority Control Function)는 시스템의 상태에 따라 각 트래픽에 우선권을 동적으로 할당하여 패킷의 스케쥴링(scheduling)을 제어하는 함수 f(.)이다. 클래스 1의 손실민감(loss-sensitive) 트래픽과 클래스 2의 지연민감(delay-sensitive) 트래픽이 고속 패킷스위치의 모든 입력포트에 동일하게 입력되고 스위칭속도(switching capacity)가 m인 $N\timesN$용량의 고속 패킷스위치에 TBPJ 방식의 DPCF 함수를 적용하여 성능을 분석하였다. 이때 스위치는 유한한 크기의 입력 버퍼와 무한크기의 출력버퍼로 구성되어 있고 슬롯 단위로 동기방식(synchronous)으로 동작한다고 가정하였다. TBPJ 방식은 각 입력버퍼에 대기하고 있는 현재 트래픽의 양과 시스템 버퍼의 문턱값(threshold)에 따라 서비스 순위를 동적으로 할당하여 효율적인 스케쥴링이 이루어지도록 한다. 성능분석을 통하여 TBPJ 제어방식이 기존의 우선권 제어 방식보다 성능 및 효율성에 있어서 우수함을 입증하였다. 즉 TBPJ 방식을 적용하여 성능을 분석한 결과 손실민감 트래픽의 QoS(Quality of Service)를 만족시키기 위하여 패킷스위치를 스위치플랜으로 구현하는 경우 병렬로 (즉 m=2) 구성하면 충분하다는 것을 확인하였다.

• 한국수학교육학회지시리즈A:수학교육
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• 제41권1호
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• pp.91-100
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• 2002

The purpose of this study is to help the students understand the concepts for the series and calculate the sum of series with diverse methods --- a) High School Algebraic Technique, b) Using Bernoulli Number, c) Integral Method, d) Euler Formular, e) Fourier Series

• 대한수학회지
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• 제44권2호
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• pp.487-498
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• 2007

In this paper, we obtain important combinatorial identities of generalized harmonic numbers using symmetric polynomials. We also obtain the matrix representation for the generalized harmonic numbers whose inverse matrix can be computed recursively.