• 제목/요약/키워드: school mathematics

검색결과 6,120건 처리시간 0.032초

Nonlinear vibration of functionally graded nano-tubes using nonlocal strain gradient theory and a two-steps perturbation method

  • Gao, Yang;Xiao, Wan-Shen;Zhu, Haiping
    • Structural Engineering and Mechanics
    • /
    • 제69권2호
    • /
    • pp.205-219
    • /
    • 2019
  • This paper analyzes nonlinear free vibration of the circular nano-tubes made of functionally graded materials in the framework of nonlocal strain gradient theory in conjunction with a refined higher order shear deformation beam model. The effective material properties of the tube related to the change of temperature are assumed to vary along the radius of tube based on the power law. The refined beam model is introduced which not only contains transverse shear deformation but also satisfies the stress boundary conditions where shear stress cancels each other out on the inner and outer surfaces. Moreover, it can degenerate the Euler beam model, the Timoshenko beam model and the Reddy beam model. By incorporating this model with Hamilton's principle, the nonlinear vibration equations are established. The equations, including a material length scale parameter as well as a nonlocal parameter, can describe the size-dependent in linear and nonlinear vibration of FGM nanotubes. Analytical solution is obtained by using a two-steps perturbation method. Several comparisons are performed to validate the present analysis. Eventually, the effects of various physical parameters on nonlinear and linear natural frequencies of FGM nanotubes are analyzed, such as inner radius, temperature, nonlocal parameter, strain gradient parameter, scale parameter ratio, slenderness ratio, volume indexes, different beam models.

한국 해역의 살오징어(Todarodes pacificus) 개체군 자원평가를 위한 베이지안 상태공간 잉여생산량 모델의 적용 (A Bayesian State-space Production Assessment Model for Common Squid Todarodes pacificus Stock Caught by Multiple Fisheries in Korean Waters)

  • 안동영;김규한;강희중;현상윤
    • 한국수산과학회지
    • /
    • 제54권5호
    • /
    • pp.769-781
    • /
    • 2021
  • Given data about the annual fishery yield of the common squid Todarodes pacificus, and the catch-per-unit-effort (CPUE) data from multiple fisheries from 2000-2018, we applied a Bayesian state - space assessment model for the squid population. One of our objectives was to do a stock assessment, simultaneously incorporating CPUE data from the following three fisheries, (i) large trawl, (ii) jigger, and (iii) large purse seine, which comprised on average a year about 65% of all fisheries, allowing possible correlations to be reflected. Other objectives were to consider both observation and process errors and to apply objective priors of parameters. The estimated annual exploitable biomass was in the range of 3.50×105 to 1.22×106 MT, the estimated intrinsic growth rate was 1.02, and the estimated carrying capacity was 1,151,259 MT. Comparison with available results from stock assessment of independently analyzed single fisheries revealed a large difference from the estimated values, suggesting that stock assessment based on multiple fisheries should be performed.

A RESULT ON AN OPEN PROBLEM OF LÜ, LI AND YANG

  • Majumder, Sujoy;Saha, Somnath
    • 대한수학회보
    • /
    • 제58권4호
    • /
    • pp.915-937
    • /
    • 2021
  • In this paper we deal with the open problem posed by Lü, Li and Yang [10]. In fact, we prove the following result: Let f(z) be a transcendental meromorphic function of finite order having finitely many poles, c1, c2, …, cn ∈ ℂ\{0} and k, n ∈ ℕ. Suppose fn(z), f(z+c1)f(z+c2) ⋯ f(z+cn) share 0 CM and fn(z)-Q1(z), (f(z+c1)f(z+c2) ⋯ f(z+cn))(k) - Q2(z) share (0, 1), where Q1(z) and Q2(z) are non-zero polynomials. If n ≥ k+1, then $(f(z+c_1)f(z+c_2)\;{\cdots}\;f(z+c_n))^{(k)}\;{\equiv}\;{\frac{Q_2(z)}{Q_1(z)}}f^n(z)$. Furthermore, if Q1(z) ≡ Q2(z), then $f(z)=c\;e^{\frac{\lambda}{n}z}$, where c, λ ∈ ℂ \ {0} such that eλ(c1+c2+⋯+cn) = 1 and λk = 1. Also we exhibit some examples to show that the conditions of our result are the best possible.

On axial buckling and post-buckling of geometrically imperfect single-layer graphene sheets

  • Gao, Yang;Xiao, Wan-shen;Zhu, Haiping
    • Steel and Composite Structures
    • /
    • 제33권2호
    • /
    • pp.261-275
    • /
    • 2019
  • The main objective of this paper is to study the axial buckling and post-buckling of geometrically imperfect single-layer graphene sheets (GSs) under in-plane loading in the theoretical framework of the nonlocal strain gradient theory. To begin with, a graphene sheet is modeled by a two-dimensional plate subjected to simply supported ends, and supposed to have a small initial curvature. Then according to the Hamilton's principle, the nonlinear governing equations are derived with the aid of the classical plate theory and the von-karman nonlinearity theory. Subsequently, for providing a more accurate physical assessment with respect to the influence of respective parameters on the mechanical performances, the approximate analytical solutions are acquired via using a two-step perturbation method. Finally, the authors perform a detailed parametric study based on the solutions, including geometric imperfection, nonlocal parameters, strain gradient parameters and wave mode numbers, and then reaching a significant conclusion that both the size-dependent effect and a geometrical imperfection can't be ignored in analyzing GSs.

A New Digital Image Steganography Approach Based on The Galois Field GF(pm) Using Graph and Automata

  • Nguyen, Huy Truong
    • KSII Transactions on Internet and Information Systems (TIIS)
    • /
    • 제13권9호
    • /
    • pp.4788-4813
    • /
    • 2019
  • In this paper, we introduce concepts of optimal and near optimal secret data hiding schemes. We present a new digital image steganography approach based on the Galois field $GF(p^m)$ using graph and automata to design the data hiding scheme of the general form ($k,N,{\lfloor}{\log}_2p^{mn}{\rfloor}$) for binary, gray and palette images with the given assumptions, where k, m, n, N are positive integers and p is prime, show the sufficient conditions for the existence and prove the existence of some optimal and near optimal secret data hiding schemes. These results are derived from the concept of the maximal secret data ratio of embedded bits, the module approach and the fastest optimal parity assignment method proposed by Huy et al. in 2011 and 2013. An application of the schemes to the process of hiding a finite sequence of secret data in an image is also considered. Security analyses and experimental results confirm that our approach can create steganographic schemes which achieve high efficiency in embedding capacity, visual quality, speed as well as security, which are key properties of steganography.

스마트 그리드를 위한 Binary CDMA 기반의 AMI 무선 네트워크 구조 및 AKA 프로토콜 (A Wireless Network Structure and AKA(Authentication and Key Agreement) Protocol of Advanced Metering Infrastructure on the Smart Grid based on Binary CDMA)

  • 전재우;임선희;이옥연
    • 정보보호학회논문지
    • /
    • 제20권5호
    • /
    • pp.111-124
    • /
    • 2010
  • 원격 검침 시스템(AMI : Advanced Metering Infrastructure)은 최근 활발히 추진 중인 스마트그리드의 핵심 인프라로, 구축비용 절감 및 운영의 효율성을 위해 무선 통신 기술 도입이 적극적으로 검토되고 있다. 하지만, AMI에 무선 통신 기술 적용 시 무선 통신의 보안 취약점 때문에 다양한 보안 위협이 발생 가능하기 때문에 이에 대한 대응책이 필요하다. 본 논문에서는 Binary CDMA 망을 이용한 AMI 네트워크 무선망 구조를 제시하고, 이에 대한 보안 대책으로 BSIM(Binary Subscriber Identity Module)을 중심으로 사용자 인증 및 무선 구간 암호화를 수행함으로써 AMI 무선 구간의 보안 위협을 감소시키는 방안에 대해 연구한다.

WDM-PON 시스템을 위한 저가격 상호 주입 잠김 F-P LD (Cost Effective Mutual Injection Locked F-P LD for WDM-PON System)

  • 황지홍;이혁재;박준모
    • 융합신호처리학회논문지
    • /
    • 제21권4호
    • /
    • pp.162-169
    • /
    • 2020
  • 본 논문에서는 엄밀한 수학 없이 상호 주임 잠김에 대한 정성적 이해를 시도하였고, 제안하는 상호 주입 잠김 광원에 대해 분석한다. 또한 두 개의 unpolarized Fabry-Perot Laser Diode (F-P LD)를 이용한 상호 주입 잠김 기반의 Wavelength Division Multiplexing - Passive Optical Network (WDM-PON)용 저가격 광원을 구현하였다. 한 쪽 F-P LD의 파장 변화에 대한 RIN (Relative Intensity Noise) 특성을 측정하였는데, 가변 파장의 범위가 2.07 nm일 때 최소 -110 dB/Hz의 RIN을 보여주었다.

MORE RELATIONS BETWEEN λ-LABELING AND HAMILTONIAN PATHS WITH EMPHASIS ON LINE GRAPH OF BIPARTITE MULTIGRAPHS

  • Zaker, Manouchehr
    • 대한수학회보
    • /
    • 제59권1호
    • /
    • pp.119-139
    • /
    • 2022
  • This paper deals with the λ-labeling and L(2, 1)-coloring of simple graphs. A λ-labeling of a graph G is any labeling of the vertices of G with different labels such that any two adjacent vertices receive labels which differ at least two. Also an L(2, 1)-coloring of G is any labeling of the vertices of G such that any two adjacent vertices receive labels which differ at least two and any two vertices with distance two receive distinct labels. Assume that a partial λ-labeling f is given in a graph G. A general question is whether f can be extended to a λ-labeling of G. We show that the extension is feasible if and only if a Hamiltonian path consistent with some distance constraints exists in the complement of G. Then we consider line graph of bipartite multigraphs and determine the minimum number of labels in L(2, 1)-coloring and λ-labeling of these graphs. In fact we obtain easily computable formulas for the path covering number and the maximum path of the complement of these graphs. We obtain a polynomial time algorithm which generates all Hamiltonian paths in the related graphs. A special case is the Cartesian product graph Kn☐Kn and the generation of λ-squares.

Optimization dynamic responses of laminated multiphase shell in thermo-electro-mechanical conditions

  • Fan, Linyuan;Kong, Degang;Song, Jun;Moradi, Zohre;Safa, Maryam;Khadimallah, Mohamed Amine
    • Advances in nano research
    • /
    • 제13권1호
    • /
    • pp.29-45
    • /
    • 2022
  • The optimization for dynamic response associated with a cylindrical shell which is made of laminated composites embedded in a piezoelectric layer which is subjected to temperature rises and is resting on an elastic foundation is investigated for the first time. The first shear order theory (FSDT) is utilized in order to obtain the strain relations of the shell. Then, using the energy method, the equations of motions as well as boundary condition of the problem are attained. The formulation of this study together with the solution procedure which is a numerical solution method, differential quadrature method (DQM) is validated using other researches. This paper presents a thorough study on the parameters which impacts the vibration frequency of the laminated shell. The results of this paper shows that any type of laminated composite shell can reduce the vibration frequency providing that the angle related to layer are higher than 85 degrees. Also, in order to reduce the effect of temperature rises, the laminated composites instead of orthotropic one can be used.

ResNet-Based Simulations for a Heat-Transfer Model Involving an Imperfect Contact

  • Guangxing, Wang;Gwanghyun, Jo;Seong-Yoon, Shin
    • Journal of information and communication convergence engineering
    • /
    • 제20권4호
    • /
    • pp.303-308
    • /
    • 2022
  • Simulating the heat transfer in a composite material is an important topic in material science. Difficulties arise from the fact that adjacent materials cannot match perfectly, resulting in discontinuity in the temperature variables. Although there have been several numerical methods for solving the heat-transfer problem in imperfect contact conditions, the methods known so far are complicated to implement, and the computational times are non-negligible. In this study, we developed a ResNet-type deep neural network for simulating a heat transfer model in a composite material. To train the neural network, we generated datasets by numerically solving the heat-transfer equations with Kapitza thermal resistance conditions. Because datasets involve various configurations of composite materials, our neural networks are robust to the shapes of material-material interfaces. Our algorithm can predict the thermal behavior in real time once the networks are trained. The performance of the proposed neural networks is documented, where the root mean square error (RMSE) and mean absolute error (MAE) are below 2.47E-6, and 7.00E-4, respectively.