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The generalized Wiener polarity index W{ink}(G) of a graph G = (V, E) is defined as a number of unordered pairs {u, v} of G such that the shortest distance between u and v is equal to k: Wk(G) = |{{u, v}, d(u, v) = k, u, v ∈ V (G)}| In this paper we give some results for 2-trees in case of mentioned index. We present an infinite family of 2-trees with maximum value of generalized Wiener polarity index.
A set function on a ground set of size n is approximately modular if it satisfies every modularity requirement to within an additive error, approximate modularity is the set analog of approximate linearity. In this paper we study how close, in additive error, can approximately modular functions be to truly modular functions. We first obtain a polynomial time algorithm that makes O(n2 log n) queries...
Most missing data analysis techniques have focused on using model parameter estimation which depends on modern statistical data analysis methods such as maximum likelihood and multiple imputation. In fact, these modern methods are better than traditional methods (for example, complete data analysis and mean imputation approaches), and in many particular applications can give unbiased parametric estimation...
The problem of minimizing the maximum of two strongly convex quadratic functions on Rn is considered. It is shown that in some cases this problem is equivalent to finding the positive root of a polynomial of the degree 2n or less.
Solution of the problem of a hinged band-shaped plate, weakened by a crack parallel to the bearings, is found. The crack is assumed to be loaded with a bending moment and shear forces. Relation between the stress intensity factor at the crack tip, crack's location, and plate's parameters has been examined.
There has been a resurgence of interest in lower bounds whose truth rests on the conjectured hardness of well known computational problems. These conditional lower bounds have become important and popular due to the painfully slow progress on proving strong unconditional lower bounds. Nevertheless, the long term goal is to replace these conditional bounds with unconditional ones. In this paper we...
We give an algorithm that, for every fixed k, decides isomorphism of graphs of rank width at most k in polynomial time. As the rank width of a graph is bounded in terms of its clique width, we also obtain a polynomial time isomorphism test for graph classes of bounded clique width.
We describe algorithms for the problem of minimum distortion embeddings of finite metric spaces into the real line (or a finite subset of the line). The time complexities of our algorithms are parametrized by the values of the minimum distortion, δ, and the spread, Δ, of the point set we are embedding. We consider the problem of finding the minimum distortion bijection...
In this paper we analyze a hash function for k-partitioning a set into bins, obtaining strong concentration bounds for standard algorithms combining statistics from each bin. This generic method was originally introduced by Flajolet and Martin [FOCS'83] in order to save a factor Ω(k) of time per element over k independent samples when estimating the number of distinct elements in a...
An (n, k)-Poisson Multinomial Distribution (PMD) is the distribution of the sum of n independent random vectors supported on the set Bk={e1,, ek} of standard basis vectors in Rk. We prove a structural characterization of these distributions, showing that, for all ε > 0, any (n, k)-Poisson multinomial random vector is ε-close, in total variation distance, to the sum...
The method of increasing the fault-tolerance of Control Unit is proposed. The main idea is to successively “contract” all values of output signals of Control Unit and to obtain final signature of convolution. It is proposed to implement the operation of division by the root polynomial (G(x) in binary Galois Field (GF)) as the convolution operation.
Recently, two novel matrices whose some entries are not syndromes and other entries are known syndromes have been presented to generate weak-locator polynomials needed in decoding the ternary quadratic residue code of length 61. This paper proposes a new unknown syndrome calculation for a class of cyclic codes and a completely algebraic decoding of the (23, 11, 9) ternary quadratic residue code up...
The S-Box operation in the Advanced Encryption Standard has a long history of research in tailored and optimised hardware designs. While Canright's design based on tower-field decomposition has long been a benchmark design for low area, designs based on linear-feedback structures achieve lower area and power consumption at the price of additional clock cycles. We combine both approaches to get a design...
In this paper, the stabilization problems for a class of Takagi-Sugeno (T-S) fuzzy neutral systems are explored. Utilizing Pólya's theorem and some homogeneous polynomials techniques, the delay-dependent stabilization condition for T-S fuzzy neutral systems are proposed in terms of a linear matrix inequality (LMI) to guarantee the asymptotic stabilization of T-S fuzzy neutral systems. Lastly, an example...
We focus on Riesz MV-algebras, which are MV-algebras equipped with a multiplication by numbers in the real interval [0,1]. In analogy with a work in preparation for MV-algebras by the same authors, we consider for every integer n the Riesz MV-algebra of all continuous functions from the n-th power of [0,1] to [0,1] and the Riesz MV-subalgebras thereof. In particular we study the Riesz MV-subalgebras...
The paper proposes a new frequency domain method for identifying linear dynamic errors-in-variables (EIV) models. The noise-free input is an arbitrary signal, not necessarily periodic and the input and output noises are additive and uncorrelated white processes. The method combines, in a frequency domain context, the characteristics of the Frisch scheme and the properties of the Yule-Walker equations...
Deformed Heun class equations or more precise Heun class equations with added apparent singularity are considered. It is proved that any deformed Heun class equation realizes under antiquantization the transfer from a Heun class equation to the corresponding Painlevé equation.
The Fast Fourier Transform (FFT) is an efficient algorithm to compute the Discrete Fourier Transform (DFT) which exploits symmetry and periodicity in the DFT. Because of its efficiency, the algorithm is implemented in many Digital Signal Processing (DSP) applications and hardware platforms for real-time applications. FFT applications also include spectrum analysis, speech processing and filter designs...
In this paper we have formulated the problem of finding an LPV-approximation to a system as an optimization problem. For this optimization problem we have presented two possible ways to solve this. The problem is posed as a model reduction problem and formulated such that it should try to preserve the input-output behavior of the system. In the two examples in the paper the potential of the new methods...
The paper describes a specific software developed within Mathematica environment. The package consists of functions that assist the solution of different modeling, analysis, and synthesis problems for nonlinear control systems. It has been made partially available over the internet using webMathematica service.
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