q-distributions and Markov processes

We consider a sequence of integer-valued random variables X_n, n 1, representing a special Markov process with transition probability λ_{n, l}, satisfying P_{n, l} = (1 − λ_{n, l}) P_{n−1, l} + λ_{n, l−1} P_{n−1, l−1}. Whenever the transition probability is given by λ_{n, l} = q^{n + βl + γ} and λ_{n, l} = 1 − q^n+βl+γ, we can find closed forms for the distribution and the moments of the corresponding random variables, showing that they involve functions such as the q-binomial coefficients and the q-Stirling numbers. In general, it turns out that the q-notation, up to now mainly used in the theory of q-hypergeometrical series, represents a powerful tool to deal with these kinds of problems. In this context we speak therefore about q-distributions. Finally, we present some possible, mainly graph theoretical interpretations of these random variables for special choices of , β and γ.     

On F-geodetic graphs

We study the graphs in which the number of geodesics between any two vertices depends only on their distance. We consider also a connection between some of thesegraphs and geodetic graphs.     

The smooth Banach submanifold B*(E, F) in B(E, F)

Let E,F be two Banach spaces,B(E,F),B+(E,F),Φ(E,F),SΦ(E,F) and R(E,F) be bounded linear,double splitting,Fredholm,semi-Frdholm and finite rank operators from E into F,respectively. Let Σ be any one of the following sets:{T ∈Φ(E,F):Index T=constant and dim N(T)=constant},{T ∈ SΦ(E,F):either dim N(T)=constant< ∞ or codim R(T)=constant< ∞} and {T ∈ R(E,F):Rank T=constant< ∞}. Then it is known that Σ is a smooth submanifold of B(E,F) with the tangent space TAΣ={B ∈ B(E,F):BN(A)-R(A) } for any A ∈Σ. However,for ...     

Challenges for mathematical and statistical modelling for metrology

There are challenges in disseminating information concerning mathematical and statistical modelling for metrology. We specify these challenges and consider ways they are being met. In addition to journal papers, the value of supporting software and other aspects are indicated. Relevant work in the UK Software Support for Metrology programme is outlined. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Tree-structured modelling of categorical predictors in generalized additive regression

Generalized linear and additive models are very efficient regression tools but many parameters have to be estimated if categorical predictors with many categories are included. The method proposed here focusses on the main effects of categorical predictors by using tree type methods to obtain clusters of categories. When the predictor has many categories one wants to know in particular which of the categories have to be distinguished with respect to their effect on the response. The tree-structured approach allows to detect clusters of categories that share the same effect while letting other predictors, in particular metric predictors, have a linear or additive effect on the response. An algorithm for the fitting is proposed and various stopping criteria are evaluated. The preferred stopping criterion is based on p values representing a conditional inference procedure. In addition, stability of clusters is investigated and the relevance of predictors is investigated by bootstrap methods. Several applications show the usefulness of the tree-structured approach and small simulation studies demonstrate that the fitting procedure works well.     

Nonequilibrium statistical operator in the generalized molecular hydrodynamics of fluids

We discuss the important role of the Zubarev nonequilibrium statistical operator method in the generalized molecular hydrodynamics of fluids. Using this method allows developing a consistent approach of generalized collective excitations for simple, ion, polar, magnetic, and some other fluids. We construct a nonequilibrium statistical operator and derive the corresponding transport equations for a system that relaxes and passes into the state of molecular hydrodynamics. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 1, pp. 91–101, January, 2008.     

On generalized statistical convergence of double sequences via ideals

The concept of statistical convergence is one of the most active area of research in the field of summability. Most of the new summability methods have relation with this popular method. In this paper we generalize the notions of statistical convergence, (λ, μ)-statistical convergence, (V, λ, μ) summability and (C, 1, 1) summability for a double sequence x = (x _jk ) via ideals. We also establish the relation between our new methods.     

A statistical generalized programming algorithm for stochastic optimization problems

In this paper, we are concerned with an algorithm which combines the generalized linear programming technique proposed by Dantzig and Wolfe with the stochastic quasigradient method in order to solve stochastic programs with recourse. In this way, we overcome the difficulties arising in finding the exact values of the objective function of recourse problems by replacing them with the statistical estimates of the function. We present the basic steps of the proposed algorithm focusing our attention on its implementation alternatives aimed at improving both the convergence and computational performances. The main application areas are mentioned and some computational experience in the validation of our approach is reported. Finally, we discuss the possibilities of parallelization of the proposed algorithmic schemes.This paper has been partially supported by the Italian MURST 40% project on Flexible Manufacturing Systems.     

Limiting behavior of the eigenvalues of a multivariate F matrix

The spectral distribution of a central multivariate F matrix is shown to tend to a limit distribution in probability under certain conditions as the number of variables and the degrees of freedom tend to infinity.     

Mathematical modelling and analysis of bulk waves in rotating generalized thermoelastic media with voids

The present paper deals with the propagation of body waves in a homogenous isotropic, rotating, generalized thermoelastic solid with voids. The complex quartic secular equation has been solved by employing Descartes’ algorithm and perturbation method to obtain phase velocities, attenuations and specific loss factors of four attenuating and dispersive waves, which are possible to exist in such media. These wave characteristics have been computed numerically for magnesium crystal and presented graphically. Statistical analysis has been performed to compare the obtained computer simulated result in order to have estimate on the suitability of the method to compute various characteristics of the waves. This work may find applications in geophysics and gyroscopic sensors.     

环Fp+vFp上互补对偶常循环码

本文研究了环F_p+vF_p上互补对偶（1-2v）-常循环码.利用环F_p+vF_p上（1-2v）-常循环码的分解式C=vC_1-v ⊕（1-v）C_v,得到了环F_p+vF_p上互补对偶（1-2v）-常循环码的生成多项式.然后借助从F_p+vF_p到F_p²的Gray映射,证明了环F_p+vF_p上互补对偶（1-2v）-常循环码的Gray像是F_p的互补对偶循环码.     

Non-linear modelling and statistical anlaysis of multi-stage high-pressure inactivation of lactic acid bacteria

It was the aim of this work to determine the combined effects of pressure, temperature, and co-solvents on Lactococcus lactis , and to detect correlations between culture-dependent and culture-independent methods for assessment of cellular viability and sublethal injury. Therefore, the pressure induced inactivation of L. lactis MG 1363 was investigated in 21 buffer systems at a pressure range of 0.1 MPa to 600 MPa and a temperature range of 5 to 50 Grad Celsius. The inactivation was characterised by viable cell counts, stress resistant cell counts, membrane integrity, metabolic activity, and LmrP activity. By using Principal Component Analysis, correlations were detected between viable cell counts and metabolic activity as well as stress resistant cell counts and LmrP activity. Based on these correlations, a fuzzy logic model was formulated. The model uses two of the five physiological states as autonomous output variables. Input variables are pressure, temperature, application time and food systems. Latter fully describe the inactivation process of L. lactis correctly. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Power of statistical tests based on generalized separable statistics in the polynomial scheme

We investigate the asymptotic properties of statistical tests using generalized separable statistics in the polynomial scheme.Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 104–111, 1986.     

Rank reversals in multi-criteria decision analysis with statistical modelling of ratio-scale pairwise comparisons

In multi-criteria decision analysis, the overall performance of decision alternatives is evaluated with respect to several, generally conflicting decision criteria. One approach to perform the multi-criteria decision analysis is to use ratio-scale pairwise comparisons concerning the performance of decision alternatives and the importance of decision criteria. In this approach, a classical problem has been the phenomenon of rank reversals. In particular, when a new decision alternative is added to a decision problem, and while the assessments concerning the original decision alternatives remain unchanged, the new alternative may cause rank reversals between the utility estimates of the original decision alternatives. This paper studies the connections between rank reversals and the potential inconsistency of the utility assessments in the case of ratio-scale pairwise comparisons data. The analysis was carried out by recently developed statistical modelling techniques so that the inconsistency of the assessments was measured according to statistical estimation theory. Several type of decision problems were analysed and the results showed that rank reversals caused by inconsistency are natural and acceptable. On the other hand, rank reversals caused by the traditional arithmetic-mean aggregation rule are not in line with the ratio-scale measurement of utilities, whereas geometric-mean aggregation does not cause undesired rank reversals.     

The generalized S-graphs of diameter 3

A graph is called a generalized S-graph if for every vertex v of G there exists exactly one vertex which is more remote from v than every vertex adjacent to v. A generalized S-graph of diameter 3 is called reducible if there is a pair of diametrical vertices v and such that v is also a generalized S-graph of diameter 3. Here we determine all irreducible generalized S-graphs of diameter 3.     

Numerical modelling and analysis of external gear pumps by applying generalized control volumes

Components in gear pumps usually involve complex geometrical arrangements in order to achieve the desired performance. The use of lumped parametric models is considered the most accurate and effective method for investigation of the associated design issues. In this study, the numerical modelling approach based on the lumped parameters and control volume concepts is reviewed, especially for gear teeth within the meshing zone. To apply the approach to the entire gear pump, control volume concepts are generalized to all gear pockets and flow orifices with some reasonable assumptions. The assumptions include instantaneous angular positions, orifice transitions and imagined control volumes with internal flows. The fluid dynamics and pump performance, which even have the measurement difficulties, can be estimated to investigate and optimize the design parameters of gears by the model. A simulation example and its experimental results of a gear machine are presented to validate the proposed approach in this article.     

A Sufficient Condition for (F1)-Effectiveness of theCT-Method

The study of (F)-effectiveness of theN_p-method was initiated by Hille and Tamarkin. In this direction, Dikshit investigated (F₁)-effectiveness of the product methodC¹N_p-method. Recently Kumar and Prasad established the necessary condition for (F₁)-effectiveness of the product method. In this note, we extend the corresponding sufficient part of Kumar and Prasad to theC¹T-method.