A simple mathematical model for free vibration analysis of combined system consisting of framed tube,shear core,belt truss and outrigger system with geometrical discontinuities

Dynamic analysis of beam-like structure is significantly important in modeling real cases such as tall buildings, aircraft wings, spacecraft antennas and many other applications. This paper tries to determine the first natural frequency of tall buildings including framed tube, shear core, belt truss and outrigger system with multiple jumped discontinuities in the cross section of framed tube and shear core. In this regard, the entire length of the tall building is partitioned into uniform segments between each two successive discontinuity points. The effect of belt truss and outrigger system is modeled as a concentrated rotational spring applied at the belt truss and outrigger system location. Many cantilevered tall structures can be treated as cantilever bars with multiple jumped discontinuities in the cross section for the analysis of their free vibration. In this paper, the continuous approach was accepted and by using the Hamilton’s variational principle, the general form of governing equation for free vibration of tall building can be obtained. By applying the separation of variable method on time and space, the governing Partial Differential Equation (PDE) of motion is reduced to an Ordinary Differential Equation (ODE) with one variable coefficient while the other coefficients are constant based on the assumption that the transverse displacement is a harmonic vibration. To find exact solution of ODE, we must have exact distribution of EI(x), AG(x), N(x) and m(x) in the height of the structure. Some of these parameters such as EI(x), AG(x) and m(x), are constant throughout the height of each segment. These parameters can be expressed exactly by using of multi criteria function, while N(x) is variable in the height of each segment. Therefore, the ODE by using the method of variable separation and partitioned method can be expressed for each segment. We must apply the continuity conditions in conjunction with different segments for obtaining unique mode shape for mentioned system. Tall building characteristics matrix can be derived based on the boundary conditions and the continuity conditions applied at the partitioned points. This matrix is particularly used to find combined system first natural frequency and mode shape. Three numerical examples with different stepped discontinuities in their cross sections are studied to demonstrate the reliability of this method. The results of the proposed mathematical model give a good understanding of the structure’s dynamic characteristics; it is easy to use, yet reasonably accurate and suitable for quick evaluations during the preliminary design stages which require less time.     

Sur le Théorème de Fubini Concernant la Réciproque du Théorème de Permutabilité de Bianchi

It is shown that Fubini’s theorem concerning the converse of Bianchi’s permutability theorem, published in 1940 in Annals of Mathematics, is true in general. There is a single exceptional case which is related to a theorem of H. Jonas, published in 1937 in Mathematische Annalen, concerningW congruences in which the necessary conditions of Fubini’s Theorem are not also sufficient. For this reason we reformulate Fubini’s theorem as follows: Letx(u, v),y(u, v) be two surfaces with a one-to-one mapping between them and such that the nets of curvesu, v on these surfaces are not osculating-related (following Jonas). If each of the three surfacesz(u, v),t(u, v),η(u, v) is a congruence transform of every one of the surfacesx(u, v),y(u, v), then the congruences generated by the lines (x, z +pt), (y, z +ρt),ρ=const are allW congruences.     

Resolution, in L-spaces, of transmission problems set in an unbounded domains

The goal of this work is to give a complete study of some abstract transmission problems (P^δ), for every δ > 0, set in unbounded domain composed of a half-line ]−∞, 0[ and a thin layer ]0, δ[. Existence and uniqueness results are obtained for strict solutions in UMD Banach spaces, by using essentially the semigroup theory and the Dore-Venni’s Theorem given in [8].     

城市表层土壤重金属污染分析模型

本文先利用Matlab做出各种重金属元素浓度的空间分布图,初步得到土壤重金属污染的状况.接着用内梅罗污染指数法定量的确定土壤重金属污染最严重的地区,并用主成分分析法进行了验证.最后利用灰色-灾变与回归预测的组合模型解决了地质环境的演变问题.     

A semiparametric Bernstein–von Mises theorem for Gaussian process priors

This paper is a contribution to the Bayesian theory of semiparametric estimation. We are interested in the so-called Bernstein–von Mises theorem, in a semiparametric framework where the unknown quantity is (θ, f), with θ the parameter of interest and f an infinite-dimensional nuisance parameter. Two theorems are established, one in the case with no loss of information and one in the information loss case with Gaussian process priors. The general theory is applied to three specific models: the estimation of the center of symmetry of a symmetric function in Gaussian white noise, a time-discrete functional data analysis model and Cox’s proportional hazards model. In all cases, the range of application of the theorems is investigated by using a family of Gaussian priors parametrized by a continuous parameter.     

A system dynamics sustainable business model for Petroleos Mexicanos (Pemex): case based on the Global Reporting Initiative

We propose a System Dynamics model to explain the implementation and development of business sustainable policies at Petroleos Mexicanos (Pemex). The model is built using information reported by this company on the Global Reporting Initiative website. The simulation model incorporates the participation and expectations of internal and external stakeholders in defining sustainability (as perceived by the organization) and implementing its initiatives. Three variables (leadership, stakeholder motivation and external factors), identified as leverage points in the model, are used as means to improve the organization's journey towards achieving sustainability. The results of the simulation model seem to indicate that by increasing leadership activity and levels of stakeholder motivation, the journey towards sustainability can be greatly improved, and that external economic factors do not have a significant impact on sustainability achievement. These findings are pertinent for organizations currently in the process of implementing sustainable policies and strategies.     

On Two Measures of Problem Instance Complexity and their Correlation with the Performance of SeDuMi on Second-Order Cone Problems

We evaluate the practical relevance of two measures of conic convex problem complexity as applied to second-order cone problems solved using the homogeneous self-dual (HSD) embedding model in the software SeDuMi. The first measure we evaluate is Renegar's data-based condition measure C(d), and the second measure is a combined measure of the optimal solution size and the initial infeasibility/optimality residuals denoted by S (where the solution size is measured in a norm that is naturally associated with the HSD model). We constructed a set of 144 second-order cone test problems with widely distributed values of C(d) and S and solved these problems using SeDuMi. For each problem instance in the test set, we also computed estimates of C(d) (using Peña’s method) and computed S directly. Our computational experience indicates that SeDuMi iteration counts and log (C(d)) are fairly highly correlated (sample correlation R = 0.675), whereas SeDuMi iteration counts are not quite as highly correlated with S (R = 0.600). Furthermore, the experimental evidence indicates that the average rate of convergence of SeDuMi iterations is affected by the condition number C(d) of the problem instance, a phenomenon that makes some intuitive sense yet is not directly implied by existing theory.     

Numerical study of transient free convective mass transfer in a Walters-B viscoelastic flow with wall suction

A transient model for the free convective, nonlinear, steady, laminar flow and mass transfer in a viscoelastic fluid from a vertical porous plate is presented. The Walters-B liquid model is employed which introduces supplementary terms into the momentum conservation equation. The transformed conservation equations are solved using the finite difference method (FDM). The influence of viscoelasticity parameter (Γ), species Grashof number (Gc), Schmidt number (Sc), distance (Y) and time (t) on the velocity (U) and also concentration distribution (C) is studied graphically. Velocity is found to increase with a rise in viscoelasticity parameter (Γ) with both time and distances close to the plate surface. An increase in Schmidt number is observed to significantly decrease both velocity and concentration in time and also with separation from the plate. Increasing species Grashof number boosts the flow velocity through all time and causes a significant rise primarily near the plate surface. The study has applications in polymer materials processing.     

Global Steady State Analytical Solution of Cadmium Uptake Model for Plant Roots

The concentration distribution of cadmium ion in soil is studied by the phytoavailability model. According to the states of the cadmium complex: fully inert, fully labile and partially labile, we establish three corresponding cadmium uptake sub-models, and derive respective global analytical solutions at steady state. In particular, when the complex is partially labile, we give the steady analytical solution of cadmium ion concentration in cylindrical geometry composed of the analytical solutions of partially labile complex and fully inert complex in planar geometry and fully inert complex in cylindrical geometry, that is, the ration approximation method. In this paper, the global analytical solutions are compared with the results of literature and numerical simulations. Therefore, the double check is realized to ensure the rationality of the analytical method. The global concentration profile of cadmium ions in the whole rhizosphere can be described by the steady state analytical solutions: the concentration of cadmium ion increases with the distance from the root surface and finally reaches the initial value; the change rate of cadmium ion concentration is the largest when the complex is fully labile; whatever the state of the complex is, cadmium ions never accumulate on the root surface. Finally, we discuss and compare the effects of moving and fixed right boundaries of the model on the results. The results show that it is more reasonable to take the fixed right boundary, and plant roots can uptake cadmium ions in a wider range.     

区间数排序法在土壤重金属生态风险分析中的应用

将土壤重金属含量以区间形式表示,并引入区间数排序法,建立了一种基于区间数排序法的土壤重金属生态风险分析模型,并对土壤重金属进行生态风险分析.结果表明,7种重金属的区间排序向量排序为PbCdAsZnCuCrNi,重金属Pb、Cd、As和Zn的生态风险较大.此分析结果符合当地的实际情况,同时与地积累指数法的结果相符,说明区间数排序法在土壤重金属生态风险分析的应用是合理的,其分析结果具有可靠性,也为土壤重金属的风险管理提供理论依据.     

On the commutant algebras corresponding to the permutation representations of the full collineation groups of PG(k,s) and EG(k,s), s = pr,k ⩾ 2

In this paper, the dimension t and a linear basis of the commutant algebra corresponding to the representation of the full collineation group as matrices permuting the flags (incident point-line or point-hyperplane pairs) have been determined for each one of the four geometries PG(2, s), EG(2, s), PG(k, s), and EG(k, s), s = p^r, k ? 3. For the four geometries, t = 6, 7, 7, and 8, respectively, and the corresponding linear bases are (I, G, B, T, BT, TB), (I, G, B, T, BT, TB, BTB), (I, G, B, T, BT, TB, S), and (I, G, B, T, BT, TB, BTB, S). I, G, B, T are the relationship matrices of James (Ann. Math. Statist.28 (1957), 993–1082) and the matrix S was introduced by Sysoev and Shaikin (Avtomat. i Telemekh.5 (1976), 64–73).     

A deteriorating multi-item inventory model with fuzzy costs and resources based on two different defuzzification techniques

Normally inventory models of deteriorating items, such as food products, vegetables, etc. involve imprecise parameters, like imprecise inventory costs, fuzzy storage area, fuzzy budget allocation, etc. In this paper, we aim to provide two defuzzification techniques for two fuzzy inventory models using (i) extension principle and duality theory of non-linear programming and (ii) interval arithmetic. On the basis of Zadeh’s extension principle, two non-linear programs parameterized by the possibility level α are formulated to calculate the lower and upper bounds of the minimum average cost at α-level, through which the membership function of the objective function is constructed. In interval arithmetic technique the interval objective function has been transformed into an equivalent deterministic multi-objective problem defined by the left and right limits of the interval. This formulation corresponds to the possibility level, α = 0.5. Finally, the multi-objective problem is solved by a multi-objective genetic algorithm (MOGA). The model has been illustrated through a numerical example and solved for different values of possibility level, α through extension principle and for α = 0.5 via MOGA. As a particular case, the results have been obtained for the inventory model without deterioration. Results from two methods for α = 0.5 are compared.     

Defining equations of modular curves

We obtain defining equations of modular curves X₀(N), X₁(N), and X(N) by explicitly constructing modular functions using generalized Dedekind eta functions. As applications, we describe a method of obtaining a basis for the space of cusp forms of weight 2 on a congruence subgroup. We also use our model of X₀(37) to find explicit modular parameterization of rational elliptic curves of conductor 37.     

Sometimes effective Thue-Siegel-Roth-Schmidt-Nevanlinna bounds,or better

This paper will do the following: (1) Establish a (better than) Thue-Siegel-Roth-Schmidt theorem bounding the approximation of solutions of linear differential equations over valued differential fields; (2) establish an effective better than Thue-Siegel-Roth-Schmidt theorem bounding the approximation of irrational algebraic functions (of one variable over a constant field of characteristic zero) by rational functions; (3) extend Nevanlinna's Three Small Function Theorem to an n small function theorem (for each positve integer n), by removing Chuang's dependence of the bound upon the relative “number” of poles and zeros of an auxiliary function; (4) extend this n Small Function Theorem to the case in which the n small functions are algebroid (a case which has applications in functional equations); (5) solidly connect Thue-Siegel-Roth-Schmidt approximation theory for functions with many of the Nevanlinna theories. The method of proof is (ultimately) based upon using a Thue-Siegel-Roth-Schmidt type auxiliary polynomial to construct an auxiliary differential polynomial.     

On large sets of disjoint steiner triple systems,V

In a previous paper (J. Combin. Theory Ser. A34 (1983), 156–182), to construct large sets of disjoint STS(3n)'s (i.e., LTS(3n)'s), a kind of combinatorial design, denoted by LD(n), where n is the order of design, was introduced and it was shown that if there exist both an LD(n) and an LTS(n + 2), then there exists an LTS(3n) also. In this paper, after having established some recursive theorems of LD(n), the following result was proved: If n is a positive integer such that n≡11 (mod 12), then there exists an LD(n), except possibly n ∈ {23, 47, 59, 83, 107, 167, 179, 227, 263, 299, 347, 383, 719, 767, 923, 1439}.     

Atoms, anti-atoms and complements in the lattice of quasi-uniformities

We describe the atoms of the complete lattice (q(X),⊆) of all quasi-uniformities on a given (nonempty) set X. We also characterize those anti-atoms of (q(X),⊆) that do not belong to the quasi-proximity class of the discrete uniformity on X. After presenting some further results on the adjacency relation in (q(X),⊆), we note that (q(X),⊆) is not complemented for infinite X and show how ideas about resolvability of (bi)topological spaces can be used to construct complements for some elements of (q(X),⊆).     

Caps in PG(n,q),q even,n⩾3

Letm′₂(3,q) be the largest value ofk(k<q ²+1) for which there exists a completek-cap in PG(3,q),q even. In this paper, the known upper bound onm′₂(3,q) is improved. We also describe a number of intervals, fork, for which there does not exist a completek-cap in PG(3,q),q even. These results are then used to improve the known upper bounds on the number of points of a cap in PG(n, q),q even,n?4.     

Continue,quit, restart probability model

We discuss a new applied probability model: there is a system whose evolution is described by a Markov chain (MC) with known transition matrix on a discrete state space and at each moment of a discrete time a decision maker can apply one of three possible actions: continue, quit, and restart MC in one of a finite number of fixed “restarting” points. Such a model is a generalization of a model due to Katehakis and Veinott (Math. Oper. Res. 12:262, 1987), where a restart to a unique point was allowed without any fee and quit action was absent. Both models are related to Gittins index and to another index defined in a Whittle family of stopping retirement problems. We propose a transparent recursive finite algorithm to solve our model by performing O(n³) operations.     

Modeling and simulation of nitrogen regulation in Corynebacterium glutamicum

Modeling the dynamic behaviour of biochemical systems at a molecular level aims at understanding and predicting the interactions of macromolecules inside the cell. Models of small subsystems based on differential equations not only prepare the way for the long-term goal of understanding a whole cell, but are inherently valuable due to their ability to predict the behaviour of the subsystem for varying external conditions or parameters. Nitrogen supply is essential for prokaryotes, thus the nitrogen uptake is an interesting target for model building. The goal is to provide new information about the interactions of the relevant proteins by performing various simulations.A model based on piecewise linear differential equations is formulated for the nitrogen uptake in Corynebacterium glutamicum. We theoretically derive a model for biochemical networks and introduce a general method for the parameter estimation which is also applicable in the case of very short time series. This approach is applied to a special system concerning the nitrogen uptake using Western blot experiments. The equations are set up for the main components of this system, the optimization problem for parameter estimation is formulated and solved, and simulations for the evaluation of the model as well as for predictions are carried out.We show that model building based on differential equations can also, when only a few measurements are performed, lead to a satisfactory model which provides valuable insights into the way it’s network components function. For example, we are able to make predictions about the maximal value of the time course as well as the steady-state level of the signal transduction protein GlnK in case of restricted activity of the proteases when considering the transition of nitrogen starvation to nitrogen excess or vice versa.