Essential gyrators and equivalence rules for 3-port function structures

It is shown that a theorem on essential gyrators presented by Rosenberg (1) and used in (2) claims too much and that the internal structure of the multiport elements of the system must be studied in order to be able to decide whether a gyrator is essentially contained in the system or not. Bond graph terminology is used (3)—(6) and a new theorem is formulated, which provides an algorithm to decide on the essentiality of a gyrator by immediate inspection of the bond graph.As a side-result of this approach some new methods for junction structure simplification can be formulated. The significance of junction 3-ports for the concept of the essential gyrator is elaborated by providing equivalence rules for all kinds of junction 3-ports and introducing a unit essential junction 3-port (ES) and a unit non-essential junction 3-port (NES). Finally the hydraulic junction is treated as an example of a physical non-potential junction, i.e. a junction congruent with an ES.     

Doubly-terminated two-variable lossless ladder networks

In this paper necessary and sufficient conditions are derived for a two-variable positive real function to be the driving-point impedance of certain classes of doubly-terminated lossless ladder networks. Specifically, two classes of networks are studied: (a) the class of networks in which the lossless structure is a cascade of p₁- and p₂-variable two-ports, each two-port having its transmission zeros at the origin and/or at infinity; (b) the class of networks in which the lossless structure is a lowpass or highpass ladder network with series arms having p₁- and p₂-type elements in series and shunt arms having the p₁- and p₂-type elements in parallel. It is indicated that via suitable transformations of the variables, conditions for many other types of ladder structures can be derived.     

LXYL-P1-2 immobilized on magnetic nanoparticles and its potential application in paclitaxel production

BackgroundLXYL-P1-2 is the first reported glycoside hydrolase that can catalyze the transformation of 7-β-xylosyl-10-deacetyltaxol (XDT) to 10-deacetyltaxol (DT) by removing the d-xylosyl group at the C-7 position. Successful synthesis of paclitaxel by one-pot method combining the LXYL-P1-2 and 10-deacetylbaccatin III-10-β-O-acetyltransferase (DBAT) using XDT as a precursor, making LXYL-P1-2 a highly promising enzyme for the industrial production of paclitaxel. The aim of this study was to investigate the catalytic potential of LXYL-P1-2 stabilized on magnetic nanoparticles, the surface of which was modified by Ni²⁺-immobilized cross-linked Fe₃O₄@Histidine.ResultsThe diameter of matrix was 20–40 nm. The K_m value of the immobilized LXYL-P1-2 catalyzing XDT (0.145 mM) was lower than that of the free enzyme (0.452 mM), and the k_cat/K_m value of immobilized enzyme (12.952 mM s⁻¹) was higher than the free form (8.622 mM s⁻¹). The immobilized form maintained 50% of its original activity after 15 cycles of reuse. In addition, the stability of immobilized LXYL-P1-2, maintained 84.67% of its initial activity, improved in comparison with free form after 30 d storage at 4°C.ConclusionsThis investigation not only provides an effective procedure for biocatalytic production of DT, but also gives an insight into the application of magnetic material immobilization technology.How to citeZou S, Chen TJ, Li DY, et al. LXYL-P1-2 immobilized on magnetic nanoparticles and its potential application in paclitaxel production. Electron J Biotechnol 2021;50.https://doi.org/10.1016/j.ejbt.2020.12.005     

Transfer function realization of a class of doubly-terminated two-variable lossless networks and their application in linear-phase 2-dimensional digital filter design

A method is presented for the design of a class of two-dimensional (2-D) stable digital filters satisfying prescribed magnitude and constant group delay specifications. The design method generates a 2-D digital transfer function which is a product of two transfer functions H₁(z₁,z₂) and H₂(z₁,z₂), corresponding to a recursive filter and a nonrecursive filter, respectively, Component H₁(z₁,z₂) ensures a wave-digital realization, that is, the design method guarantees the generation of a corresponding analog function H_1A(s₁,s₂) which is realizable as the transfer function of a doubly-terminated two-variable lossless network. Thus the design technique ensures that not only is a given frequency response achieved, but also the generated transfer function is realizable as a cascade of a wave-digital filter and a nonrecursive digital filter. The class of filters considered here is one in which the doubly-terminated analog network used to realize the wave digital filter is a cascade of s₁- and s₂-variable lossess two-ports with all their transmission zeros at infinity.     

Stability criteria for certain classes of nonlinear difference equations

The general mth order difference equation X(n+m)+a₁X(n+m?1)+…+a_mX(n) = F[n,X(n),…,X(n+m?1)] is considered. The stability properties of its solutions are studied using the discrete form of Liapunov's direct method. A quadratic form is selected as a possible Liapunov function V(n,X) and a scheme is developed for determining appropriate conditions on this function to insure that its total difference ΔV(n,X) is negative semi-definite or negative definite with respect to the difference equation. The approach is applied to the fourth-order difference equation in full detail to illustrate the method for determining the conditions which imply either uniform stability or uniform asymptotic stability and specific results are obtained. Several comments on, and extensions of, the work done by Puri and Drake for the cases m = 2 and m = 3 are presented.The results of the present approach in the homogeneous case where F[n,X(n),…,X(n+m?1)] = 0 are compared with the usual Schur-Cohn criteria and are shown to be at least as good.     

A test for robust Hurwitz stability of convex combinations of complex polynomials

In this paper we present a method for testing the Hurwitz property of a segment of polynomials (1−λ)p₀(s)+λp₁(s), where λ∈[0,1] and p₀(s) and p₁(s) are nth-degree polynomials with complex coefficients. The method consists in constructing a parametric Routh-like array with polynomial entries and generating Sturm sequences for checking the absence of zeros of two real λ-polynomials of degrees 2 and 2n in the interval (0,1). The presented method is easy to implement. Moreover, it accomplishes the test in a finite number of arithmetic operations because it does not invoke any numerical root-finding procedure.     

Positive-real systems under lossless transformations: Invariants and reduced order models

In this paper, positive-real systems under lossless positive-real transformations are investigated. Let G(s) be the transfer function matrix of a continuous-time positive-real system of order n and F(s) a lossless transfer function of order n_F. We prove here that the lossless positive-real transformed system, i.e. G(F(s)), is also positive-real. Furthermore, the stochastic balanced representation of positive-real systems under lossless positive-real transformations is considered. In particular, it is proved that the positive-real characteristic values π_j of G(F(s)) are the same of G(s) each with multiplicity n_F, independently from the choice of F(s). This property is exploited in the design of reduced order models based on stochastic balancing. Finally, the proposed technique is a passivity preserving model order reduction method, since it is proven that the reduced order model of G(F(s)) is still positive-real. An error bound for truncation related to the invariants π_j is also derived.     

Dielectrophoresis based discrimination of human embryonic stem cells from differentiating derivatives

Assessment of the dielectrophoresis (DEP) cross-over frequency (f_xo), cell diameter, and derivative membrane capacitance (C_m) values for a group of undifferentiated human embryonic stem cell (hESC) lines (H1, H9, RCM1, RH1), and for a transgenic subclone of H1 (T8) revealed that hESC lines could not be discriminated on their mean f_xo and C_m values, the latter of which ranged from 14 to 20 mF/m². Differentiation of H1 and H9 to a mesenchymal stem cell-like phenotype resulted in similar significant increases in mean C_m values to 41–49 mF/m² in both lines (p < 0.0001). BMP4-induced differentiation of RCM1 to a trophoblast cell-like phenotype also resulted in a distinct and significant increase in mean C_m value to 28 mF/m² (p < 0.0001). The progressive transition to a higher membrane capacitance was also evident after each passage of cell culture as H9 cells transitioned to a mesenchymal stem cell-like state induced by growth on a substrate of hyaluronan. These findings confirm the existence of distinctive parameters between undifferentiated and differentiating cells on which future application of dielectrophoresis in the context of hESC manufacturing can be based.     

Stable denominators for the simplification of z-Transfer Functions

A well-known discrete stability test is used to derive from the denominator D(z) of a given stable high-order transfer function G(z), the denominator of a low-order approximant of G(z). The proposed method, based on the truncation and inversion of a continued fraction formed with the coefficients of D(z), yields a reduced denominator d(z) of degree, say m, which is always stable. Furthermore, depending on the neglected parts of the continued fraction, d(z) approximates m₁ and m₂ = m−m₁ zeros of D(z), located very near the points z=1 and z=-1, respectively. In the special case m₁=m, d(z) is identical to the polynomial obtained by applying to D(z) the indirect technique, which combines the bilinear transformation with the Routh or the Schwarz approximation method.     

VCO sweep-rate limit for a phase-lock loop

Phase-lock loops (PLLs) serve important roles in phase-lock receivers, coherent transponders, and similar applications. For many of these uses, the bandwidth of the loop must be kept small to limit the detrimental influence of noise, and this requirement makes the natural PLL pull-in phenomenon too slow and/or unreliable. For each such case, the phase-lock acquisition process can be aided by the application of an external sweep voltage to the loop voltage controlled oscillators (VCOs). The goal is to have the applied sweep voltage rapidly decrease the closed-loop frequency error to a point where phase lock occurs quickly. For a second-order loop containing a perfect integrator loop filter, there is a maximum VCO sweep-rate magnitude, denoted here as R_m rad/s², for which phase lock is guaranteed. If the applied VCO sweep rate is less than R_m, the loop cannot sweep past a stable phase-lock point, and it will phase lock. On the other hand, for an applied sweep-rate magnitude that is greater than R_m, the PLL may sweep past a lock point and fail to phase lock. In the existing PLL literature, only a trial-and-error approach has been described for estimating R_m, given values of loop damping factor ζ and natural frequency ω_n. Furthermore, no plots exist of computed versus ζ and versus ζ (B_L denotes loop-noise bandwidth). These deficiencies are dealt with in this paper. A new iterative numerical technique is given that converges to the maximum sweep-rate magnitude R_m. It is used to generate data for plots of and versus ζ, the likes of which have never appeared before in the PLL literature.     

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.     

Microfluidic chip for fast bioassays��evaluation of binding parameters

A seven channel polystyrene (PS) microchip has been constructed using a micromilling machine and a high-temperature assembling. Protein A (PA) has been immobilized by a passive sorption on the microchannel walls. Two bioaffinity assays with human immunoglobulin G (hIgG) as a ligand have been carried out. (i) PA as the receptor and fluorescently labeled hIgG (FITC-hIgG) as the ligand, (ii) PA as the receptor with hIgG as the quantified ligand and fluorescently labeled goat anti-human IgG (FITC-gIgG) as the secondary ligand. One incubation step of the assays took only 5 min instead of hours typical for enzyme-linked immunosorbent assay applications. Calibration curves of the dependence of a fluorescence signal on the hIgG concentration in a sample have been obtained in one step due to a parallel arrangement of microchannels. A mathematical model of the PA-FITC-hIgG complex formation in the chip has been developed. The values of the kinetic constant of the PA-FITC-hIgG binding (k_on=5.5 m³ mol⁻¹ s⁻¹) and the equilibrium dissociation constant of the formed complex (K_d≤3×10⁻⁶ mol m⁻³) have been obtained by fitting to experimental data. The proposed microchip enables fast evaluation of kinetic and equilibrium constants of ligand-receptor bioaffinity pairs and the ligand quantification. As the use of microfluidic chips for immunoassays is often limited by price, we used procedures and chemicals that allow for an inexpensive construction and operation of the microdevice, e.g., temperature assembling as a fabrication technique, detection via an ordinary digital camera, nonspecific polystyrene as a substrate, passive sorption of biomolecules as an immobilization technique, etc.     

Two-element type normal n-ports

A new classification of RLC reciprocal n-ports in normal and non-normal systems is proposed. The normal systems exhibit the most natural generalization of the scalar RLC one-ports; they admit canonic synthesis representations.Let R, L and C be open loop parameters of an RLC reciprocal n-port with m = n dynamically linearly independent loops. For a normal system R, L and C must commute pairwise. Alternatively, the Hermitian components of Z(s) shall commute. There exists a complete set of common orthonormal eigenvectors for R, L and C. With respect to this coordinate system the normal n-port admits a canonic structure.A normal n-port can be canonically synthesized by a unit R, L and C and an adequate supply of ideal transformers. Such decoupling is not realizable for non-normal n-ports.     

Walsh Operational Matrices for Fractional Calculus and Their Application to Distributed Systems

The Walsh operational matrix for performing integration and solving state equations is generalized to fractional calculus for investigating distributed systems. A new set of orthogonal functions is derived from Walsh functions. By using the new functions, the generalized Walsh operational matrices corresponding to √s, √(s²+ 1), e^-s and e^-√s etc. are established. Several distributed parameter problems are solved by the new approach.     

Synthesis of RC transfer immittance functions with a minimum number of capacitors

In this paper a method for the realization of RC transfer immittance functions with an unsymmetrical lattice is presented. The method yields minimal capacitor realizations for Z₁₂(s) with no pole at s = 0 and ?y₁₂(s) having no pole at s = ∞. The number of resistors needed are only two more than the minimum needed.     

The Normal Family of Linear Systems

The normal family of linear (time-variant) n-ports is introduced as the most natural extension of ordinary scalar driving-point immittance behaviour. The normality induces a certain symmetry and simplicity which merits due emphasis in future n-port research investigations. As an application of the concept of normality the overdamped-underdamped criterion is extended to n-ports. Also, an interesting problem of maximal power transfer is solved and the absolute energy invariant index calculated. This paper invites attention to the development of circuit synthesis procedures based on the algebraic structure of the normal family.     

H∞ control of periodic piecewise polynomial time-varying systems with polynomial Lyapunov function

In this paper, the H_∞ control problem of periodic piecewise systems with polynomial time-varying subsystems is addressed. Based on a periodic Lyapunov function with a continuous time-dependent Lyapunov matrix polynomial, the H_∞ performance is studied. The result can be easily reduced to the conditions for periodic piecewise systems with constant subsystems or linear time-varying systems based on a common Lyapunov function or a linear time-varying Lyapunov matrix. Moreover, an H_∞ controller with time-varying polynomial controller gain is proposed as well, which could be directly solved with the linear matrix inequalities. A numerical example is presented to demonstrate the effectiveness of the proposed method.     

s-grams: Defining generalized n-grams for information retrieval

n-grams have been used widely and successfully for approximate string matching in many areas. s-grams have been introduced recently as an n-gram based matching technique, where di-grams are formed of both adjacent and non-adjacent characters. s-grams have proved successful in approximate string matching across language boundaries in Information Retrieval (IR). s-grams however lack precise definitions. Also their similarity comparison lacks precise definition. In this paper, we give precise definitions for both. Our definitions are developed in a bottom-up manner, only assuming character strings and elementary mathematical concepts. Extending established practices, we provide novel definitions of s-gram profiles and the L₁ distance metric for them. This is a stronger string proximity measure than the popular Jaccard similarity measure because Jaccard is insensitive to the counts of each n-gram in the strings to be compared. However, due to the popularity of Jaccard in IR experiments, we define the reduction of s-gram profiles to binary profiles in order to precisely define the (extended) Jaccard similarity function for s-grams. We also show that n-gram similarity/distance computations are special cases of our generalized definitions.     

Stability and L2-gain analysis for switched neutral systems with mixed time-varying delays

This paper considers the stability and L₂-gain for a class of switched neutral systems with time-varying discrete and neutral delays. Some new delay-dependent sufficient conditions for exponential stability and weighted L₂-gain are developed for a class of switching signals with average dwell time. These conditions are formulated in terms of linear matrix inequalities (LMIs) and are derived by employing free weighting matrices method. As a special case of such switching signals, we can obtain exponential stability and normal L₂-gain under arbitrary switching signals. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results.     

Temperature distribution in toroidal electrical coils of rectangular cross section

The essential content of a recent paper by the present writer comprises a comprehensive discussion of the physical bases underlying derivation of formulas for calculating the temperature distribution T, maximum temperature T_m and average temperature T_a in a toroidal electrical coil of rectangular cross section, internally generated heat and change of wire resistance with temperature being taken into account. Illustratively, the solution for the boundary value condition of constant surface temperature and uniform equivalent thermal conductivity was obtained.For the most part, however, problems that arise in practice are not encompassed in the comparatively simple boundary conditions of constant temperature. Experiment shows that in general the boundary condition is $\text{T ? T′ = ?}\text{K?}\text{?n}$; whereof n denotes the outward drawn normal to the coil surface, $\text{K = (}\text{k}{}_{\mathrm{n}}\text{h}\text{)}$ the ratio of the equivalent thermal conductivity in the direction of n to the emissivity of the boundary surface, and T and T′ are the corresponding temperatures in the coil surface and the immediately adjacent ambient medium. Again, it frequently ensues in practice that the thermal conductivity is substantially different in the directions of the two principal axes of the cross section.In the present paper formulas for T, T_m, and T_a are obtained for electrical coils of ratio of external to internal radius greater than (roughly) two whereof (i) the thermal conductivity is different in the directions of the two principal axes of the cross section, (ii) K is different on but constant over each of the four faces of the coil, and (iii) no restriction is made as to T′ except that over each face it be expressible in a generalized Fourier series. Determination of T is posed as a boundary-value problem in the mathematical theory of heat; the formal solution of T effected by expansions in orthogonal functions; and T_m and T_a then determined through use of their known relationships with T. The resulting formulas are in the form of rapidly-converging singly-infinite trigonometric-hyperbolic series. Illustrative of application of these general formulas, the maximum temperatures in a coil of given dimensions subject to two different sets of surface conditions are calculated and found to be in excellent agreement with the known measured values.The just-mentioned formulas encompass practically all cases encountered in practice except those coils which do not satisfy the restriction as to ratio of radii. For these latter formulas for T, T_m, and T_a are obtained pursuant to conditions of (i) equivalent thermal conductivity different in the directions of the two principal axes of the cross section, (ii) K, and likewise T′, different on but constant over each of the four faces of the coil. These formulas are in the form of rapidly-converging singly-infinite trigonometric- Bessel function (of zero order) series: Illustratively, the maximum temperature in a coil of given dimensions is calculated and found to be in excellent agreement with the known measured value.