Random Structures & Algorithms Author Index to Volume 3

We consider statistically homogeneous two-phase random piezoactive structures with deterministic properties of inclusions and the matrix and with random mutual location of inclusions. We present the solution of a coupled stochastic boundary value problem of electroelasticity for the representative domain of a matrix piezocomposite with a random structure in the generalized singular approximation of the method of periodic components; the singular approximation is based on taking into account only the singular component of the second derivative of the Green function for the comparison media. We obtain an analytic solution for the tensor of effective properties of the piezocomposite in terms of the solution for the tensors of effective properties of a composite with an ideal periodic structure or with the "statistical mixture" structure and with the periodicity coefficient calculated for a given random structure with its specific characteristics taken into account. The effective properties of composites with auxiliary structures (periodic and "statistical mixture") are also determined in the generalized singular approximation by varying the properties of the comparisonmedium. We perform numerical computations and analyze the effective properties of a quasiperiodic piezocomposite with reciprocal polarization of oriented ellipsoidal inclusions and the matrix, the layered structures with reciprocal polarization of the layers [1] of a polymer piezoelectric PVF, and find their unique properties such as a significant increase in the Young modulus along the normal to the layers and in dielectric permittivities, the appearance of negative values of the Poisson ratio under extension along the normal, and an increase in the absolute values of the basic piezomoduli.

Previous article Next article Random Partitions of SetsV. N. SachkovV. N. Sachkovhttps://doi.org/10.1137/1119019PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Leo Moser and , Max Wyman, An asymptotic formula for the Bell numbers, Trans. Roy. Soc. Canada. Sect. III. (3), 49 (1955), 49–54 MR0078489 (17,1201c) 0066.31001 Google Scholar[2] V. N. Sachkov, Distribution of the number of distinct elements of a symmetric basis in a random $mA$-sample, Theory Prob. Applications, 16 (1971), 494–505 10.1137/1116053 0263.60002 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Combinatorial Models of the Distribution of Prime Numbers27 May 2021 | Mathematics, Vol. 9, No. 11 Cross Ref On the maximal multiplicity of block sizes in a random set partitionRandom Structures & Algorithms, Vol. 56, No. 3 Cross Ref Random partitions of a set with given number of blocksDiscrete Mathematics and Applications, Vol. 13, No. 3 Cross Ref Random Set Partitions: Asymptotics of Subset CountsJournal of Combinatorial Theory, Series A, Vol. 79, No. 2 Cross Ref Some Probabilistic Aspects of Set Partitions10 April 2018 | The American Mathematical Monthly, Vol. 104, No. 3 Cross Ref Random Set PartitionsWilliam M. Y. Goh and Eric Schmutz17 February 2012 | SIAM Journal on Discrete Mathematics, Vol. 7, No. 3AbstractPDF (1107 KB)On sets of integers with prescribed gapsMonatshefte f�r Mathematik, Vol. 116, No. 2 Cross Ref Gap-Free Set Partitions11 October 2006 | Random Structures & Algorithms, Vol. 3, No. 1 Cross Ref Generation of a random partition of a finite set by an urn modelJournal of Combinatorial Theory, Series A, Vol. 35, No. 2 Cross Ref Counting subsets of the random partition and the 'Brownian Bridge' processStochastic Processes and their Applications, Vol. 15, No. 2 Cross Ref Volume 19, Issue 1| 1974Theory of Probability & Its Applications History Submitted:14 February 1973Published online:28 July 2006 InformationCopyright © 1974 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1119019Article page range:pp. 184-190ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

Diode-pumped multi-mode graded-index (GRIN) fiber Raman lasers provide prominent brightness enhancement both in linear and half-open cavities with random distributed feedback via natural Rayleigh backscattering. Femtosecond laser-inscribed random refractive index structures allow for the sufficient reduction in the Raman threshold by means of Rayleigh backscattering signal enhancement by +50 + 66 dB relative to the intrinsic fiber level. At the same time, they offer an opportunity to generate Stokes beams with a shape close to fundamental transverse mode (LP01), as well as to select higher-order modes such as LP11 with a near-1D longitudinal random structure shifted off the fiber axis. Further development of the inscription technology includes the fabrication of 3D ring-shaped random structures using a spatial light modulator (SLM) in a 100/140 μm GRIN multi-mode fiber. This allows for the generation of a multi-mode diode-pumped GRIN fiber random Raman laser at 976 nm with a ring-shaped output beam at a relatively low pumping threshold (~160 W), demonstrated for the first time to our knowledge.

Nanoparticles (NPs) offer a promising approach in modern medicine for the treatment of various diseases. They serve as effective carriers for various drugs including antibiotics, antivirals and anticancer agents. Hyaluronic acid-based nanoparticles (HA-NPs) have been interested owing to their exceptional biocompatibility and biodegradability. Hyaluronic acid (HA) is a natural biopolymer with versatile applications. However, there have been limited numbers of studies on molecular simulations of nanoparticles, particularly HA-NPs. In this study, molecular dynamics simulations were employed to explore molecular models representing the assembly of HA-NPs. Two types of HA-NPs, acetylated hyaluronic acid nanoparticles (AcHA-NPs) and hyaluronic acid-ceramide nanoparticles (HACe-NPs), were assessed for their stability and drug adsorption ability by varying the size and number of HA chains to form the nanoparticle under different conditions. The findings of the study revealed that the AcHA-NP model adopted a random or amorphous structure, whereas the HACe-NP exhibited a well-organized micelles-like structure. Both types of HA-NPs demonstrated potential drug carriers, as doxorubicin molecules were able to bind. It is important to note that AcHA-NP lacked of specific binding site due to its random structure whereas the drug clustered around the hydrophobic core of the HACe-NP.

We obtain simple, but rigorous bounds for impurity quantum states, for a tight-z binding model on random fractal structures. From these we conclude that a “typical” state on a percolation cluster decays with Euclidean distance r as exp [- cra], with 1 ⩽ a ⩽ ξ̃c, where rξ̃c is the average chemical distance. Averaging over all random configurations yields regular exponential decay, a = 1. Our bounds indicate that the probability of a classical random walker to reach distance r at time t decays as exp [- (rd/w/t)α], t < rdw, with 1/(dw - 1) ⩽ α ⩽ ξ̃c/(dw - ξ̃c). For the fully averaged probability we expect α = 1/(dw - 1). The thermally activated hopping conductivity between impurities on a random structure with fractal dimensionality D is found to behave as exp [- (T0/T)β], with β = ξ̃c/(D + ξ̃c).

A certificate of authenticity (COA) is an inexpensive physical object that has a random unique structure with high cost of near-exact reproduction. An additional requirement is that the uniqueness of COA's random structure can be verified using an inexpensive device. Bauder was the first to propose COA created as a randomized augmentation of a set of fixed-length fibers into a transparent gluing material that randomly fixes once for all the position of the fibers within. Recently, Kirovski (2004) showed that linear improvement in the compression ratio of a point-set compression algorithm used to store fibers' locations, yields exponential increase in the cost of forging a fiber-based COA instance. To address this issue, in this paper, we introduce a novel, generalized heuristic that compresses M points in an N-dimensional grid with computational complexity proportional to O(M/sup 2/). We compare its performance with an expected lower bound. The heuristic can be used for numerous other applications such as storage of biometric patterns.

Topology Optimization of Biomimetic Cellular Polymeric Materials with Random Structure Based on Strain Energy

For a sequence of random structures with n-element domains over a relational signature, we define its FO complexity as a certain subset in the Banach space ℓ∞/c0. The well-known FO zero-one law and FO convergence law correspond to FO complexities equal to {0, 1} and a subset of R, respectively. We present a hierarchy of FO complexity classes, introduce a stochastic FO reduction that allows to transfer complexity results between different random structures, and deduce using this tool several new logical limit laws for binomial random structures. Finally, we introduce a conditional distribution on graphs, subject to a FO sentence ϕ, that generalises certain well-known random graph models, show instances of this distribution for every complexity class, and prove that the set of all ϕ validating 0--1 law is not recursively enumerable.

A honeycomb-ring hybrid random mesh structure is designed to achieve low stray light performance. The honeycomb-ring hybrid random mesh comprises the random honeycomb and random ring, achieving two random superpositions in the structure distribution. The stray light distribution is very low by the combination design with different random hybrid structures. In order to illustrate the advantages of the hybrid random structure, we design a random honeycomb network by randomly offsetting vertices. At the same time, for the random honeycomb structure, we replace each vertex with the ring structure with the size of the ring randomly controlled. Thus, the corresponding honeycomb-ring hybrid random structure is obtained. Compared with the random honeycomb, the maximal normalized high-order diffraction energy of the honeycomb-ring hybrid random mesh is about a 62.85% drop, and the shielding performance is increased by about 50%. At the same time, the optical transmittance remains nearly unchanged. Due to the enjoyable property of the designed honeycomb-ring hybrid random mesh, a sample was prepared for performance verification. The measurement results show that it achieves eminent diffraction pattern distribution with the maximal normalized high-order diffraction energy of about -31.8 dB. At the same time, the average optical transmittance exceeds 86%, and the electromagnetic shielding effectiveness (SE) in the Ku band is greater than 26 dB. Based on the fine photoelectric performance of the honeycomb-ring hybrid random mesh structure, it has great application potential for high-quality optical windows.

The correlation-extremum systems theory is extended to stochastic systems with random structure or with switching parameters and the new suboptimal (due to the nonlinear system state and measurement equations) filtering and parameter identification algorithms and their linearized form are derived, which provide adaptive features and reliable operation for the proposed combined correlation-extremum dynamic systems with random structure under environment influences, and represent new solutions of the linearization problem for the case of great estimation errors. The obtained linearized solution allows the simplification of the filter a priori performance investigation at the signal processing system design stage.

A general multivariate mixed effect linear model is introduced. Special cases of the model include the multivariate nested error covariance component regression and the random coefficient repeated measure model. Discussion is given on modeling the random effect structure and its effect on statistical inference. A procedure for testing certain class of hypotheses concerning the random effect structure is developed. The procedure is based on a statistic in a readily computable form, facilitating the use at the model building stage. 1. The Model. This paper is concerned with introducing a general multivariate mixed effect model, and with developing a procedure for testing hypotheses concerning the random effect structure in such a model. For simplicity we concentrate here on mixed models with the one-way random effect structure, i.e., with the random effect (other than the error term) involving one unknown covariance matrix. To introduce our general model, first consider the most widely used univariate mixed effect model with the one-way classification random effect or with the nested error structure. The response yij and the k ? 1 explanatory variable Xij for the j-th individual in the z-th group are assumed to satisfy

The topological and metric properties of a few natural 2D random cellular structures, namely an armadillo shell structure and young soap froths, which are formed from two classes of cells, large and small, have been characterized. The topological properties of a model generated from a Kagome tiling, which mimics such random binary structures, have also been exactly calculated. The distribution of the number of cell sides is bimodal for the structures investigated. In contrast to the classical Aboav-Weaire law for homogeneous 2D random cellular structures, nm(n), the mean total number of edges of neighbouring cells of cells with n sides does not vary linearly with n. Only the nm(i, n) (i = 1, 2) determined separately for every class of cells are linear in n for all investigated structures. Topological properties and correlations between metric and topological properties are finally compared with the predictions of various literature models.

Developed is a self-consistent statistical mechanics approach for determining the effective dynamic elastic and diffraction properties of the composites with random structures. The problem is reduced to the model of a single inclusion with a inhomogeneous elastic neighbourhood in a medium with the effective dynamic elastic properties. The inhomogeneous elastic properties and size of the neighbourhood are defined by probabilistic laws for the inclusion distribution in a representative domain. Numerical results are given for the effective dynamic elastic properties and for the effective section of the scattering of the composite with unidirectional hollow fibres.

Structural characterization of proteins in wheat flour doughs enriched with intermediate wheatgrass (Thinopyrum intermedium) flour

The susceptibility in arbitrary directions, the specific heat, the energy and the magnetization of general Ising-type chains are exactly expressed in terms of the eigenvectors of the transfer matrix corresponding to the Ising-type interaction. These quantities, as a result, can be explicitly obtained for small spin values and generally obtained from the solution of corresponding eigenvalue problem of finite degree. Numerical estimations are easy for arbitrary spin values. This formula includes the spin- S transverse Ising model with vanishing or non-vanishing parallel external field, the Blume-Emery-Griffiths model and the Blume-Capel model, mixed spin and mixed bond periodic systems such as alternating Ising chains or Ising ferrimagnets and also includes Ising models with random structures. Low temperature behaviors of these systems and the crossover to infinite spin systems are also investigated.