A multivariable bounded-reality criterion

The multivariable approach to the synthesis of networks composed of a finite number of uniform lossless transmission lines, commensurable or incommensurable, and lumped passive elements is verified by showing that the multivariable rational matrix, W(λ₀,λ₁, .. ,λn) is bounded real in (n + 1) complex variables if and only if W is bounded real in p after substituting, λ₀ = α₀p + β₀ and λ_i = tanh (α_ip + β_i) for λ_i (1?i?n) where all the α's and β's are nonnegative and arbitrary, except for being not simultaneously zero in like indexed pairs. Consequences of this result are discussed.     

Stability of oscillations in systems obeying Mathieu's equation

Numerous relatively simple physical systems give rise under appropriate circumstances to oscillations which obey the equation y″ + ?(1 + k cos t)y = 0 (Mathieu's equation). These oscillations may be either stable, periodic, or unstable, depending upon parameters of the physical system as expressed by the parameters ? and k in the basic equation. It has been customary to distinguish between the stable and unstable states by diagrams of the type of Fig. 1, from which it is possible to tell whether a given set of values of the parameters ?, k will yield a stable or unstable solution. In this paper are given curves which not only present this information, but in addition give for an important part of the stable state the values of the characteristic exponent μ. The solution of the equation y″ + ?(1 + k cos t)y = 0 depends to a large extent on this exponent, and the availability of values of μ should greatly facilitate the practical application of the equation.     

The inverse lure problem of optimal control

Given the linear system $\text{x}\text{}$ = Ax - bu, y = c^Tx, it is shown that, for a certain non-quadratic cost functional, the optimal control is given by u_opt(x) = h(c^Tx), where the function h(y) must satisfy the conditions ky²?h(y)y>0 for y≠0, h(0) = 0 and existence of h^-1 everywhere. The linear system considered must satisfy the Popov condition 1/k + (1 +?ωβ) G(?ω)>0 for all ω, G(s) being the y(s)/u(s) transfer function.     

Stabilities and Settling Times of Nonlinear and Time-varying Feedback Systems

The bounded-input bounded-output stability, finite time stability and settling time of a single-loop feedback system consisting of a nonlinear time-varying gain followed by a linear time-invariant system are investigated via a nonlinear integral inequality. The gain has the form k₀+k₁(t)+k₂(t)g(bd) where g(bd) is a monotonic increasing function. The system is bounded-input bounded-output stable provided the time-varying gains are L¹(0, t8) functions and is finite time stable for bounded gains. The nonlinear integral inequality, which is used to obtain explicit and useful bounds on the output of the system, is also employed to determine the settling time.     

Alternative convergence criteria for iterative methods of solving nonlinear equations

Let χ_m+1=T(χ_m) or even χ_m+1=T(χ_m,χ_m?1, …, χ_m?q), m=1,2,3 … be an iteration method for solving the nonlinear problem F(χ)=0, where F(χ) and its derivatives possess all of the properties required by T(χ_m). Then if it can be established that for the problem at hand ∥F(χ_m+1)∥?β_m∥F(χ_m)∥, ? m > M₀ (M₀<∞) and 0?β_m<1 , definitions are established and theorems proven concerning convergence, uniqueness and bounds on the error after ‘m’ successive iterations of a new approach to convergence properties T(χ_m). These charateristics are referred to as “alternate” (local, global) convergence properties and none of the proofs given are restricted to any specific type of method such as, e.g. contraction mapping types. Application of results obtained are illustrated using Newton's method as well as the general concept of Newton-like methods.     

Cutoff wavenumbers and the field of surface wave modes of an eccentric circular Goubau waveguide

The cutoff wavenumbers k_nm and the field of surface wave modes of a circular cylindrical conductor eccentrically coated by a dielectric are determined analytically. The electromagnetic field is expressed in terms of circular cylindrical wave functions referred to both axes, in combination with related addition theorems. When the solutions are specialized to small eccentricities kd, where d is the distance between the two axes, exact closed-form expressions are obtained for the coefficients g_nm in the resulting relation k_nm(d)=k_nm(0)[1+g_nm(k_nmd)²+...] for the cutoff wavenumbers of the waveguide. Similar expressions are obtained for the field. Numerical results for all types of modes are given. For certain values of the parameters, it is possible to enhance the operating bandwidth of the basic hybrid mode HE₁₁ over the conventional concentric guide.     

Log-periodic quantum magneto-oscillations and discrete-scale invariance in topological material HfTe5

Discrete-scale invariance (DSI) is a phenomenon featuring intriguing log-periodicity that can be rarely observed in quantum systems. Here, we report the log-periodic quantum oscillations in the longitudinal magnetoresistivity (ρ_xx) and the Hall traces (ρ_yx) of HfTe₅ crystals, which reveal the DSI in the transport-coefficients matrix. The oscillations in ρ_xx and ρ_yx show the consistent logB-periodicity with a phase shift. The finding of the logB oscillations in the Hall resistance supports the physical mechanism as a general quantum effect originating from the resonant scattering. Combined with theoretical simulations, we further clarify the origin of the log-periodic oscillations and the DSI in the topological materials. This work evidences the universality of the DSI in the Dirac materials and provides indispensable information for a full understanding of this novel phenomenon.     

Mathematical models of information system use

This report presents the results from a study of mathematical models relating to the usage of information systems. For each of four models, the papers developed during the study provide three types of analyses: reviews of the literature relevant to the model, analytical studies, and tests of the models with data drawn from specific operational situations. (1) The Cobb-Douglas model: x₀ = ax₁^bx₂^(1?b).This classic production model, normally interpreted as applying to the relationship between production, labor, and capital, is applied to a number of information related contexts. These include specifically the performance of libraries, both public and academic, and the use of information resources by the nation's industry. The results confirm not only the utility of the Cobb-Douglas model in evaluation of the use of information resources, but demonstrate the extent to which those resources currently are being used at significantly less than optimum levels. (2) Mixture of Poissons:

$\text{χ}{}_0\text{=}\text{∑}\text{i=0}\text{n}\text{i}\text{∑}\text{j=0}\text{p}\text{n}{}_{\mathrm{j}}\text{e}{}^{\mathrm{mj}}\text{(m}{}_{\mathrm{j}}\text{)′/i!}$

where x₀ is the usage and (n_j,m_j),j = 0 to p, are the p + 1 components of the distribution. This model of heterogeneity is applied to the usage of library materials and of thesaurus terms. In each case, both the applicability and the analytical value of the model are demonstrated. (3) Inverse effects of distance: x = a e^?md if c(d) = rdx = ad^?m if c(d) = r log(d).These two models reflect different inverse effects of distance, the choice depending upon the cost of transportation. If the cost,c(d), is linear, the usage is inverse exponential; if logarithmic, the usage is inverse power. The literature that discusses the relationship between usage of facilities and the distance from them is reviewed. The models are tested with data from the usage of the Los Angeles Public Library, both Central Library and branches, based on a survey of 3662 users. (4) Weighted entropy:

$\text{S(x}{}_1\text{,x}{}_2\text{,...,x}{}_{\mathrm{n}}\text{)= -}\text{∑}\text{i=1}\text{n}\text{r(x}{}_{\mathrm{i}}\text{P(x}{}_{\mathrm{i}}\text{)}\text{log}\text{(p(x}{}_{\mathrm{i}}\text{)).}$

This generalization of the “entropy measure of information” is designed to accommodate the effects of “relevancy”, as measured by r(x), upon the performance of information retrieval systems. The relevant literature is reviewed and the application to retrieval systems is considered.     

On recursive averaging processes and Hilbert space extensions of the contraction mapping principle

If T maps a convex domain D_T into itself, and if {ω_n} is a real sequence with range in (0, 1] then the recursive averaging process,

$\text{X}{}_{\mathrm{n+1}}\text{=(1?omega;}{}_{\mathrm{n}}\text{)}\text{X}{}_{\mathrm{n}}\text{+ω}{}_{\mathrm{n}}\text{+ω}{}_{\mathrm{n}}\text{T}\text{x}{}_{\mathrm{n}}\text{,}\text{x}{}_0\text{=ξ?D}{}_{\mathrm{T}}$

generates a sequence {x?_n}; with range in D_T. Under suitable conditions on D_T, T and {ω_n} the sequence {x?_n} will converge in some sense to a fixed point of T. We prove that if D_T is a closed convex subset of a complex Hilbert space H, if Tω = (1 ? ω) I + ωT is a strict contraction for some ω ? (0, 1], and if {ω_n} satisfies the conditions,

$\text{ω}{}_{\mathrm{n}}\text{→ 0}$

and

$\text{∑}\text{n=0}\text{∞}\text{ω}{}_{\mathrm{n}}\text{=∞}$

then, for arbitrary ξ ? D_T, {x?_n} converges strongly to (the unique) fixed point of T. We also prove that if D_T and {ω_n} satisfy the foregoing conditions, if T has at least one fixed point, and if Tω is non-expansive for some ω ? (0, 1], then for all ξ ? D_T, {x?_n} converges at least weakly to some fixed point of T. Finally, we apply these results to linear equations involving bounded normal operators and obtain an extension of the classical Neumann operator series.     

Strategy of oxygen transfer coefficient control on the l-erythrulose fermentation by newly isolated Gluconobacter kondonii

BackgroundThe effect of diverse oxygen transfer coefficient on the l-erythrulose production from meso-erythritol by a newly isolated strain, Gluconobacter kondonii CGMCC8391 was investigated. In order to elucidate the effects of volumetric mass transfer coefficient (k_La) on the fermentations, baffled and unbaffled flask cultures, and fed-batch cultures were developed in present work.ResultsWith the increase of the k_La value in the fed-batch culture, l-erythrulose concentration, productivity and yield were significantly improved, while cell growth was not the best in the high k_La. Thus, a two-stage oxygen supply control strategy was proposed, aimed at achieving high concentration and high productivity of l-erythrulose. During the first 12 h, k_La was controlled at 40.28 h^-1 to obtain high value for cell growth, subsequently k_La was controlled at 86.31 h^-1 to allow for high l-erythrulose accumulation.ConclusionsUnder optimal conditions, the l-erythrulose concentration, productivity, yield and DCW reached 207.9 ± 7.78 g/L, 6.50 g/L/h, 0.94 g/g, 2.68 ± 0.17 g/L, respectively. At the end of fermentation, the l-erythrulose concentration and productivity were higher than those in the previous similar reports.     

Lectin in agglutination and its role in detection of sugars on the surface of RBC of normal and cancer patients

In the present studies the property of Lectins as agglutinin and to bind sugars in the blood on normal and cancer cervix patients has been studied. Out of 36 lectins extracted from the seeds of various plants, 25 were non-specific haemagglutinins and 11 were non-reactive with the RBC of normal persons. The titre value greatly varied from 1∶4 to 1∶4096. The titre value of RBC of patients of carcinoma cervix (Stage III) was compared with the normal person’s RBC. Out of 25 non-specific haemagglutinins 16 lectins did not show any difference in titre value. Nine lectins agglutinated RBC of cancer patient at a higher dilution than the normal. On the contrary, 3 lectins agglutinated the cancerous patient’s RBC at a higher concentration than the normal (Control). Sugar specificity of 25 non-specific haemagglutinins was tested with 13 sugars separately. Haemagglutination Inhibition (HI) reaction showed marked difference in the RBC of normal and in carcinoma cervix patient. Four marked reactions were noticed. RBC of normal (N) and carcinoma patient (C) with positive HI reaction (C₊/N₊), with negative HI reaction (C_?/N_?); with C positive and N negative HI reaction (C₊/N_?) and with C negative and N positive HI reaction (C_?/N₊). Three lectins were specific to sugar moieties.Vicia faba JV II showed dissimilarity with fructose and glucose moiety and also indicated that cellulose is common in both RBC of normal and cancer cervix patient.Triticum vulgare lectin showed the difference in cellulose moiety.Linum usitatissimum lectin showed the difference in lactose moiety and indicated that melibiose is present in both. It was also observed that mannose gave positive HI reaction with lectins ofR. communis, L. esculentus, P. sativum, P. sativum Pusa 10,P. sativum R?1,D. lablab, A. indica, H. vulgare andZ. mays in the blood of cancer cervix patient suggesting that mannose perhaps is present in the RBC while it may not be present in the normal person’s RBC. Raffinose also gave the positive HI reaction with cancer patient’s blood and not with the normal person’s blood.     

A new approach to the design of coupling networks

Mathematical results are derived, which enable one to find a vector of parameters k⁰ such that (P₁(s,k⁰)?H)∩(P₂(k⁰)=0), where P₁(s,k) is a polynomial in s and in the components of k,P₂(k) is a polynomial in the components of k, and H is the set of Hurwitz polynomials. The algorithm is based on an extension of the root locus technique to the multiparameter case. The design problem of coupling networks between a resistive generator and a passive load, under prescribed power gain characteristics, is translated into the above formulation. A numerical example is provided.     

上海市通勤高碳排放群体识别与特征分析

近年来,居民交通需求的扩大导致交通领域的碳排放量不断增加。而通勤作为交通出行的刚性需求,对碳排放有重要影响。基于2013年"上海居民生活碳消费状况调查"中的交通出行数据,本文测算并深入分析了上海市常住居民的日通勤碳排放量及分布情况。结果显示,上海市常住居民人均通勤碳排放量为1 213.9g/日,个体间差异巨大,20%的通勤群体碳排放量占总通勤碳排放的80.6%。本文结合发达国家的交通碳排放情况和调研的实际情况,将人均通勤碳排放量3 000g/日及以上的个人定义为显著高碳排放者,此类人群约占总样本量的11.5%;而将目前碳排放量低于3 000g/日,但选择高碳出行方式的个人定义为潜在高碳排放者。通过有序多项Logistic回归分析发现,显著的通勤高碳排放者主要是男性群体,而潜在的高碳排放者受接送孩子等家庭因素的影响更多,且多为远郊区的居民。收入和受教育水平高是通勤显著高碳排放者和潜在高碳排放者的共同特征。     

A general equation of state: Equations for ammonia and steam

This paper is a continuation of a previous paper published in this JOURNAL. The basic idea in the two papers is to enlarge the assemblage of thermodynamic states by including the so-called “metastable” states. Considering a system, in one or two phases, which has a single type of transformation, the writer develops an equation of state of the form η = a + by + cp + dpv + (e + fv + gp + hpv) In T, where p, v, T are three independent variables, and a, b, c, etc. are constants.The latent heat at p, T = constant is λ_P,T = I (v₂ -v₁) [b+db+(f+hp) InT), which is derived from the equation of state.The available thermodynamic data on ammonia and steam are used to check these equations. It is found that within the saturated region the agreement is quite satis factory, whereas for the superheated region the agreement is not so good.     

A useful identity in circuit theory

A useful identity expressing the derivative of an unknown variable x_k of X with respect to an entry in the coefficient matrix of a linear system AX = B is presented. If the derivatives of x_k with respect to each entry of A or their combinations are required, then the identity avoids the repeated solution of the linear equations, and may result in a symbolic solution provided A^-1 is known. A method to measure the sensitivity in an n-port linear system is proposed, and its relationships to Kron's method of tearing and Branin's formulae are also discussed.     

Some New Convergence Conditions for Jacobi's Method

Let Aχ = b be a linear system or equations in which A is an n × n matrix and both χ and b are n dimensional column vectors. If in addition A is row diagonally predominant (i.e. for any i, ¦:a_ii¦>¦:a_ij¦: for all 1?j?n,i≠j), then criteria are developed to show how to ascertain when such matrix problems may be successfully solved using Jacobi's iterative method.     

“信息人”假设及其现实意义

信息需求和信息行为是人与生俱来的本能,我们是“信息人”。人类经历了从自发“信息人”到自觉“信息人”的转变过程,成为“理性信息人”。“理性信息人”是具有强烈“信息欲”的人,是追求“充分信息”的人。“信息人”假设具有重要的现实意义,推动人类社会从物质时代走向信息时代。