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On a conjecture related to the ruin probability for nonhomogeneous insurance claims

References [1] Assmussen, S. and Albrecher, H., Ruin Probabilities, World Scientific Publishing Co., Singapore, 2010. [2] Blazevicius, K.; Bieliauskiene, E. and Siaulys, J., Finite-time ruin probability in the inhomogeneous claim case, Lithuanian Mathematical Journal 50 (3), 2010, 260-270. [3] Castaner, A.; Claramunt, M.M.; Gathy, M.; Lefevre, C. and Marmol, M., Ruin problems for a discrete time risk model with non-homogeneous conditions, Scandinavian Actuarial Journal (2), 2013, 83-102. [4] De

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Another approach to the evaluation of a certain multivariate compound distribution

-75. [4] R. Grubel and R. Hermesmeier, Computation of compound distributions I: aliasing errors and exponential tilting, ASTIN Bull., 29(2) (1999), 197-214. [5] T. Jin and J. Ren, Recursions and fast Fourier transforms for a new bivariate aggregate claims model, Scand. Actuar. J., 2014(8) (2014), 729-752. [6] N.L. Johnson, S. Kotz and N. Balakrishnan, Discrete Multivariate Distributions, Wiley, New York, 1997. [7] S.A. Klugman, H.H. Panjer and G.E. Willmot, Loss Models: From Data to Decisions, 2nd edn., Wiley

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Corrigendum to secret sharing on infinite graphs

Abstract

The proof of Claim 6.8 in the Appendix of [L. Csirmaz: Secret sharing on infinite graphs, Tatra Mt. Math. Publ. 41 (2008), 1-18] is incorrect. Here we give a new (and hopefully correct) proof.

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A multi-dimensional FBSDE with quadratic generator and its applications

Abstract

We consider, in the Markovian framework, a multi-dimensional forward - back - ward stochastic differential equation with quadratic growth for the generator function of the backward system. We prove an existence result of the solution and we use this result for pricing and hedging of contingent claims that depend on non-tradeable indexes by portfolios consisting in correlated risky assets.

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Hardware optimizations of stream cipher rabbit

ABSTRACT

Stream ciphers form part of cryptographic primitives focused on privacy. Synchronous, symmetric and software-oriented stream cipher Rabbit is member of final portfolio of European Union's eStream project. Although it was designed to perform well in software, employed operations seem to compute effi­ciently in hardware. 128-bit security, with no known security weaknesses is claimed by Rabbit's designers. Since hardware performance of Rabbit was only estimated in the proposal of algorithm, comparison of direct and optimized FPGA im­plementations of Rabbit stream cipher is presented, identifying algorithm bot­tlenecks, discussing optimization techniques applied to algorithm computations, along with key area/time trade-offs.

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Relationship Between Hyper MV -algebras and Hyperlattices

Abstract

Sh. Ghorbani, et al. [9], generalized the concept of MV -algebras and defined the notion of hyper MV -algebras. Now, in this paper, we try to prove that any hyper MV -algebra is a hyperlattice. First we prove that any hyper MV -algebra that satisfies the semi negation property is a hyperlattice. Then with a computer program, we show that any hyper MV -algebra of order less than 6, is a hyperlattice. Finally, we claim that this result is correct for any hyper MV -algebra.

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Fast convergence of the Coiflet-Galerkin method for general elliptic BVPs

We consider a general elliptic Robin boundary value problem. Using orthogonal Coifman wavelets (Coiflets) as basis functions in the Galerkin method, we prove that the rate of convergence of an approximate solution to the exact one is O(2 −nN ) in the H1 norm, where n is the level of approximation and N is the Coiflet degree. The Galerkin method needs to evaluate a lot of complicated integrals. We present a structured approach for fast and effective evaluation of these integrals via trivariate connection coefficients. Due to the fast convergence rate, very good approximations are found at low levels and with low Coiflet degrees, hence the size of corresponding linear systems is small. Numerical experiments confirm these claims.

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Some remarks on evaluating the quality of the multiple sequence alignment based on the BAliBASE benchmark

Some remarks on evaluating the quality of the multiple sequence alignment based on the BAliBASE benchmark

BAliBASE is one of the most widely used benchmarks for multiple sequence alignment programs. The accuracy of alignment methods is measured by bali_score—an application provided together with the database. The standard accuracy measures are the Sum of Pairs (SP) and the Total Column (TC). We have found that, for non-core block columns, results calculated by bali_score are different from those obtained on the basis of the formal definitions of the measures. We do not claim that one of these measures is better than the other, but they are definitely different. Such a situation can be the source of confusion when alignments obtained using various methods are compared. Therefore, we propose a new nomenclature for the measures of the quality of multiple sequence alignments to distinguish which one was actually calculated. Moreover, we have found that the occurrence of a gap in some column in the first sequence of the reference alignment causes column discarding.

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Simple Graphs as Simplicial Complexes: the Mycielskian of a Graph

Summary

Harary [10, p. 7] claims that Veblen [20, p. 2] first suggested to formalize simple graphs using simplicial complexes. We have developed basic terminology for simple graphs as at most 1-dimensional complexes.

We formalize this new setting and then reprove Mycielski’s [12] construction resulting in a triangle-free graph with arbitrarily large chromatic number. A different formalization of similar material is in [15].

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Monitoring of Eating Habits and Physical Activity Levels as a Basis for a new Noncommunicable Disease Prevention Programme in the Republic of Macedonia

Abstract

Research evidence on health determinants has led to development of a national programme for noncommunicable disease (NCD) prevention. Numerous studies have confirmed the role of nutrition and physical activity in preventing main NCDs: cardiovascular disease, type 2 diabetes, cancer and chronic respiratory disease. The aim of the study was to analyse and evaluate the results obtained from the new “cross-sectional” study in 2012 offer monitoring of eating habits and physical activity levels monitoring related to socioeconomic status of the participants in 2012. The study was conducted in five regions of the Republic of Macedonia and included 1600 respondents aged 10 to 64 years. Monitoring was conducted using self-designed questionnaire. Eating habits were surveyed using questionnaires to monitor the frequency of consumption of main food groups during a week. Leisure time physical activity was a priority measure in the study. Also, in the study a model was applied for strategic planning in NCD prevention, based on the results of the health behaviour survey. The model was analysed using a software package. The results indicate that NCDs prevention through improving physical activity levels and changes in eating habits should be focused on changes in food content including availability of whole grain bread, guidelines and policy on food labelling and health claims, marketing and city planning that facilitates an active life.

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