Small deviations of iterated processes in space of trajectories

We derive logarithmic asymptotics of probabilities of small deviations for iterated processes in the space of trajectories. We find conditions under which these asymptotics coincide with those of processes generating iterated processes. When these conditions fail the asymptotics are quite different

Composition of processes and related partial differential equations

In this paper different types of compositions involving independent fractional Brownian motions B^j_{H_j}(t), t>0, j=1,$ are examined. The partial differential equations governing the distributions of I_F(t)=B^1_{H_1}(|B^2_{H_2}(t)|), t>0 and J_F(t)=B^1_{H_1}(|B^2_{H_2}(t)|^{1/H_1}), t>0 are derived by different methods and compared with those existing in the literature and with those related to B^1(|B^2_{H_2}(t)|), t>0. The process of iterated Brownian motion I^n_F(t), t>0 is examined in detail and its moments are calculated. Furthermore for J^{n-1}_F(t)=B^1_{H}(|B^2_H(...|B^n_H(t)|^{1/H}...)|^{1/H}), t>0 the following factorization is proved J^{n-1}_F(t)=\prod_{j=1}^{n} B^j_{\frac{H}{n}}(t), t>0. A series of compositions involving Cauchy processes and fractional Brownian motions are also studied and the corresponding non-homogeneous wave equations are derived.Comment: 32 page

Randomly Stopped Nonlinear Fractional Birth Processes

We present and analyse the nonlinear classical pure birth process \mathpzc{N} (t), $t>0$, and the fractional pure birth process \mathpzc{N}^\nu (t), $t>0$, subordinated to various random times, namely the first-passage time $T_t$ of the standard Brownian motion $B(t)$, $t>0$, the $\alpha$-stable subordinator \mathpzc{S}^\alpha(t), $\alpha \in (0,1)$, and others. For all of them we derive the state probability distribution $\hat{p}_k (t)$, $k \geq 1$ and, in some cases, we also present the corresponding governing differential equation. We also highlight interesting interpretations for both the subordinated classical birth process \hat{\mathpzc{N}} (t), $t>0$, and its fractional counterpart \hat{\mathpzc{N}}^\nu (t), $t>0$ in terms of classical birth processes with random rates evaluated on a stretched or squashed time scale. Various types of compositions of the fractional pure birth process \mathpzc{N}^\nu(t) have been examined in the last part of the paper. In particular, the processes \mathpzc{N}^\nu(T_t), \mathpzc{N}^\nu(\mathpzc{S}^\alpha(t)), \mathpzc{N}^\nu(T_{2\nu}(t)), have been analysed, where $T_{2\nu}(t)$, $t>0$, is a process related to fractional diffusion equations. Also the related process \mathpzc{N}(\mathpzc{S}^\alpha({T_{2\nu}(t)})) is investigated and compared with \mathpzc{N}(T_{2\nu}(\mathpzc{S}^\alpha(t))) = \mathpzc{N}^\nu (\mathpzc{S}^\alpha(t)). As a byproduct of our analysis, some formulae relating Mittag--Leffler functions are obtained

Kentsel dış mekanlarda yer alan heykel ve benzeri plastik elemanların peyjaz mimarlığı açısından incelenmesi üzerine bir araştırma

TEZ1786Tez (Yüksek Lisans) -- Çukurova Üniversitesi, Adana, 1994.Kaynakça (s. 154-160) var.xi, 162 s. : rnk. res. ; 30 cm.

TRANSIENT ANOMALOUS SUB-DIFFUSION ON BOUNDED DOMAINS

This paper develops strong solutions and stochastic solutions for the tempered fractional diffusion equation on bounded domains. First the eigenvalue problem for tempered fractional derivatives is solved. Then a separation of variables and eigenfunction expansions in time and space are used to write strong solutions. Finally, stochastic solutions are written in terms of an inverse subordinator

On a backward problem for multidimensional Ginzburg-Landau equation with random data

In this paper, we consider a backward in time problem for the Ginzburg Landau equation in a multidimensional domain associated with some random data. The problem is ill-posed in the sense of Hadamard. To regularize the instable solution, we develop a new regularized method combined with statistical approach. We prove an upper bound on the rate of convergence of the mean integrated squared error in L2 and H1 norms

On a backward problem for multidimensional Ginzburg-Landau equation with random data

In this paper, we consider a backward in time problem for the Ginzburg Landau equation in a multidimensional domain associated with some random data. The problem is ill-posed in the sense of Hadamard. To regularize the instable solution, we develop a new regularized method combined with statistical approach. We prove an upper bound on the rate of convergence of the mean integrated squared error in L2 and H1 norms

Failed orchiopexy - Leading causes and surgical management

Introduction: Failure after orchiopexy or cryptorchidism after inguinal surgery are not so rarely encountered conditions. Reoperative orchiopexies are technically demanding procedures. In our study, we aimed to examine the causes of failures and outcomes of reorchiopexies. Patients and Methods: Between 1993 and 2003, a total of 28 children who underwent reoperative orchiopexy were included into the study. Undescended testes was detected as unilateral in 24 and bilateral in 4 cases. The mean age of patients at the time of second operation was 6.8 years. The mean period of time between the first and the second operations was 3.2 ( 1 - 13 years) years. Results: The first operations were orchiopexies in all patients. After the first operations, 15 testes were found to be localized at the high scrotal position, 8 at the level of the external ring and 9 within the inguinal canal. Overall, reorchiopexies were performed on 32 testes in 28 patients. During the second operation, patent processus vaginalis was detected in 11 (34.4%), and unsuccessful hernia repair in 9 (28.1%) cases. After reorchiopexies, two testes with preoperative inguinal location could only be brought to high scrotal position and in another case orchiectomy was performed to an atrophic testis. Overall, after a mean follow-up period of 3.8 ( 1 - 7 years) years following the second operations, 29 (93.5%) testes were scrotal without evidence of atrophy. Conclusion: In our series, inadequate repair of inguinal hernia or patent processus vaginalis, as noted in 62.5% of the cases, was determined as an important factor leading to failure after surgical treatment of undescended testis. Adequate dissection and correction of inguinal hernia increase the success rate after orchiopexies. Copyright (C) 2004 S. Karger AG, Basel