Optimal Filtering of an Advertising Production System with Deteriorating Items

In this paper, we consider an integrated stochastic advertising-production system in the case of a duopoly. Two firms spend certain amounts to advertise some product. The expenses processes evolve according to the jumps of two homogeneous, finite-state Markov chains. We assume that the items in stock may be subject to deterioration and the deterioration parameter is assumed to be random

Numerical Stability of the GSXO Orthogonalization Scheme

The main focus of this thesis is on orthogonalization schemes specifically GSXO. In Chapter 3 (in particular, Section 3.2), we will analyze each step of the GSXO algorithm. The details of all constants were discussed thoroughly. It should be emphasized that these details were unfortunately missing in the pertinent literature. We were obligated to do so since in any inductive process, they may conduce to a substantial quantity. Given an m by n matrix A, GSXO computes Q of the same dimension. In Theorem 3.3.1, we will establish a bound on the error in each column. In Theorem 3.6.5, we will illustrate that under the mild condition of 400mn 3 2 u&kappa;(A) &lt; 1, GSXO computes Q such that, kI &minus; QTQk2 &le; 66mn 3 2 &kappa;(A)u � &kappa;(A) = &sigma;max(A) &sigma;min(A) , &sigma;max(A), &sigma;min(A) are maximum and minimum singular values resepctively, and u is the machine precision, matrices A, and Q are input and output of the algorithm, respectively� . The last result would allow us to prove the final piece of stability criterion which is representativity. In Chapter 4, we will apply the recent work of Higham which is error analysis under stochastic model of computation. We will show that for five different steps, we can obtain tighter bounds with high probability and applicable to low precision computation. This is the first work in analyzing the QR factorization algorithms under stochastic model of computation. [43]. In Chapter 5, we will offer two propositions relating least squares problem to the product of singular values. Thereafter, we will prove a theorem about condition number under the existence of noise. Next, we will offer four different methods to bound the atomic part of the problem, which is, kX + Y k2 (X is a fixed vector, and Y is a random vector). Two of these methods will be applied to prove results about orthogonal projection, least squares problem, and condition number problem. These results will be applied to prove two theorems about GSXO under the existence of noise, with no assumption on the condition number. Chapter 6 was done in collaboration with Pereira, and Langou. In Chapter 6, we will analyze different algorithms for generating Givens rotations, and compare them via both theoretical worstcase scenario and numerical experiments. Furthermore, we will offer a new algorithm which is more accurate than its competitors.</p

Multifocal Primary Non- Hodgkin’s Lymphoma of the Oral Cavity: Report of Three Cases and Review of the Literature

Objective: Oral non- Hodgkin’s lymphoma (NHL) is a relatively rare neoplasm that may develop in the soft tissues or jaw bones, with or without node or marrow involvement. Oral lymphomas  are often difficult to diagnose as there are no characteristic clinical features and usually appear as non- tender swellings.Case: We describe clinical, radiographic, histopathological and immunohistochemical findings of three cases of multifocal NHLs presenting in the oral cavity.Conclusion: If the oral lesion is multifocal, extra nodal lymphoma must be considered in the differential diagnosis

A Large Orthokeratinized Odontogenic Cyst of the Maxilla: A Rare Case Report

Objectives Orthokeratinized odontogenic cysts (OOCs) are relatively uncommon odontogenic cysts, lined by an orthokeratinized epithelium. These cysts show different clinical behaviors from the more common odontogenic keratocysts (OKCs), and it is important to distinguish these two types of cysts. Commonly, OOCs manifest as well-defined, unilocular, radiolucent lesions, with a high frequency in the mandibular region. In this case report, we aimed to describe a large maxillary OOC with prominent tooth displacement. Case The patient was a 14-year-old boy with significant painless swelling in the upper jaw. The panoramic radiograph revealed a well-defined, unilocular radiolucent area from midline to the first right maxillary molar with prominent tooth displacement. The lesion was completely excised under local anesthesia. The histopathological sections demonstrated a cystic lesion lined by an orthokeratinized stratified squamous epithelium with a prominent granular cell layer. Conclusion Based on the present results, OOCs can be large in size and may be characterized by ballooning expansion and tooth displacement. Therefore, knowledge of the clinical and radiographic features of these uncommon odontogenic cysts can facilitate an accurate diagnosis