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# Large forbidden configurations and design theory

Studia Scientiarum Mathematicarum Hungarica
Authors: R. P. Anstee and Attila Sali

Let forb(m, F) denote the maximum number of columns possible in a (0, 1)-matrix A that has no repeated columns and has no submatrix which is a row and column permutation of F. We consider cases where the configuration F has a number of columns that grows with m. For a k × l matrix G, define s · G to be the concatenation of s copies of G. In a number of cases we determine forb(m, m α · G) is Θ(m k). Results of Keevash on the existence of designs provide constructions that can be used to give asymptotic lower bounds. An induction idea of Anstee and Lu is useful in obtaining upper bounds.

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# Mixed-type reverse order laws for the group inverses in rings with involution

Studia Scientiarum Mathematicarum Hungarica
Authors: Dijana Mosić and Dragan S. Djordjević

We investigate some equivalent conditions for the reverse order laws (ab)# = b a # and (ab)# = b # a in rings with involution. Similar results for (ab)# = b # a* and (ab)# = b*a # are presented too.

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# A survey of product posterior distributions

Studia Scientiarum Mathematicarum Hungarica

In Bayesian statistics, one frequently encounters priors and posteriors that are product of two probability density functions. In this paper, we discuss three such priors/posteriors, provide motivation and derive expressions for their moments, median and mode. Forty seven motivating examples are discussed. We expect that this paper could serve as a useful reference for practitioners of Bayesian statistics. It could also encourage further research in this area.

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# Characterization of power function distribution based on spacings

Studia Scientiarum Mathematicarum Hungarica
Authors: G. G. Hamedani and H. W. Volkmer

A characterization of power function distribution based on the distribution of spacings is presented here extending the existing characterizations of the uniform distribution in this direction.

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# Conditional oscillation of Euler type half-linear differential equations with unbounded coefficients

Studia Scientiarum Mathematicarum Hungarica
Authors: Jaroslav Jaroš and Michal Veselý

The oscillatory properties of half-linear second order Euler type differential equations are studied, where the coefficients of the considered equations can be unbounded. For these equations, we prove an oscillation criterion and a non-oscillation one. We also mention a corollary which shows how our criteria improve the known results. In the corollary, the criteria give an explicit oscillation constant.

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# Existence of periodic solutions of fourth-order p-Laplacian difference equations

Studia Scientiarum Mathematicarum Hungarica
Authors: Haiping Shi, Xia Liu, and Yuanbiao Zhang

By making use of the critical point theory, the existence of periodic solutions for fourth-order nonlinear p-Laplacian difference equations is obtained. The main approach used in our paper is a variational technique and the Saddle Point Theorem. The problem is to solve the existence of periodic solutions of fourth-order nonlinear p-Laplacian difference equations. The results obtained successfully generalize and complement the existing one.

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# Existence results for a second order nonlocal boundary value problem at resonance

Studia Scientiarum Mathematicarum Hungarica
Author: Katarzyna Szymańska-Dȩbowska

The paper focuses on existence of solutions of a system of nonlocal resonant boundary value problems $x″=f(t,x), x′(0)=0, x(1)=∫01x(s)dg(s)$, where f : [0, 1] × ℝk → ℝk is continuous and g : [0, 1] → ℝk is a function of bounded variation. Imposing on the function f the following condition: the limit limλ→∞ f(t, λ a) exists uniformly in aS k−1, we have shown that the problem has at least one solution.

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# The solvability of some nonlinear functional integral equations

Studia Scientiarum Mathematicarum Hungarica
Authors: İsmet Özdemir and Ümit Çakan

In this paper, using a Darbo type fixed point theorem associated with the measure of noncompactness we prove a theorem on the existence of solutions of some nonlinear functional integral equations in the space of continuous functions on interval [0, a]. We give also some examples which show that the obtained results are applicable

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# Strong approximation of Black-Scholes theory based on simple random walks

Studia Scientiarum Mathematicarum Hungarica
Authors: Zsolt Nika and Tamás Szabados

A basic model in financial mathematics was introduced by Black, Scholes and Merton in 1973. A classical discrete approximation in distribution is the binomial model given by Cox, Ross and Rubinstein in 1979. In this work we give a strong (almost sure, pathwise) discrete approximation of the BSM model using a suitable nested sequence of simple, symmetric random walks. The approximation extends to the stock price process, the value process, the replicating portfolio, and the greeks. An important tool in the approximation is a discrete version of the Feynman-Kac formula as well.

Our aim is to show that from an elementary discrete approach, by taking simple limits, one may get the continuous versions. We think that such an approach can be advantageous for both research and applications. Moreover, it is hoped that this approach has pedagogical merits as well: gives insight and seems suitable for teaching students whose mathematical background may not contain e.g. measure theory or stochastic analysis.

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# Turán type inequalities for confluent hypergeometric functions of the second kind

Studia Scientiarum Mathematicarum Hungarica
Authors: Árpád Baricz, Saminathan Ponnusamy, and Sanjeev Singh

In this paper we deduce some tight Turán type inequalities for Tricomi confluent hypergeometric functions of the second kind, which in some cases improve the existing results in the literature. We also give alternative proofs for some already established Turán type inequalities. Moreover, by using these Turán type inequalities, we deduce some new inequalities for Tricomi confluent hypergeometric functions of the second kind. The key tool in the proof of the Turán type inequalities is an integral representation for a quotient of Tricomi confluent hypergeometric functions, which arises in the study of the infinite divisibility of the Fisher-Snedecor F distribution.

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