Solution of Differential Equations with Applications to Engineering Problems

Over the last hundred years, many techniques have been developed for the solution of ordinary differential equations and partial differential equations. While quite a major portion of the techniques is only useful for academic purposes, there are some which are important in the solution of real problems arising from science and engineering. In this chapter, only very limited techniques for solving ordinary differential and partial differential equations are discussed, as it is impossible to cover all the available techniques even in a book form. The readers are then suggested to pursue further studies on this issue if necessary. After that, the readers are introduced to two major numerical methods commonly used by the engineers for the solution of real engineering problems

On the Generalized Bertrand Curves in Euclidean NN-spaces

In this article, we give a necessary condition for a $C^\infty$-special Frenet curve in $\mathbb{R}^{N}$ being a generalized Bertrand curve

Evaluation of Wood Quality of Taiwania Trees Grown with Different Thinning and Pruning Treatments Using Ultrasonic-Wave Testing

The variations of Vtree, Vlumber, MOEtree, and MOElumber in the thinning and pruning treatments showed the similar trend. Results of this study also demonstrate that the effect of silvicultural practices on wood properties can be identified with the ultrasonic-wave properties of trees. This indicates that this non-destructive ultrasonic-wave technique can be provided basic information for future management practice and wood utilization of Taiwania

Crushing Strength Sampling With Minimal Damage to Taiwania (Taiwania Cryptomerioides) Using a Fractometer

The Fractometer is a device that stresses radial increment cores in the direction of the fiber to measure crushing strength, which can provide a direct wood quality indicator for structural lumber. This study analyzes the pattern of the radial variation in Taiwania (Taiwania cryptomerioides Hay.) trunk wood crushing strength to explore its effect on the precision and efficiency of the sampling procedure in the outer increment core zone as an alternate nondestructive sampling method. A pith-to-bark 0.5-cm caliber core was extracted at breast height (1.3 m above the ground) from each tree and was separated into individual section groups. Then individual crushing strengths were determined using the Fractometer.In this study, the variation in crushing strength in the transverse direction increased from the pith outward to the bark side. An analysis of variance and correlation analysis were used to evaluate the data. The magnitude of the radial variation in crushing strength was smaller than the tree-to-tree variation. Including samples of at least 7.2 cm, 5.4 cm, and 2.4 cm near the bark side was found to be acceptable for the assessment of wood crushing strength for trees of Type A (DBH > 27 cm), Type B (DBH = 23~27 cm), and Type C (DBH > 23 cm), respectively

Building Cooperation in VoIP Network through a Reward Mechanism

In this paper, for solving the moral hazard problem of super nodes in VOIP network and achieving better communication quality, we establish a reward mechanism based on classical efficiency-wage models. In the reward mechanism, the function of reward is to encourage super nodes to contribute their bandwidth and cover their effort costs, whereas the function of fine is to prevent opportunistic super nodes from shirking. We consider that network quality and idle bandwidth are the essential criterions for selecting qualified super nodes. Once all super nodes can satisfy specific conditions, the required reward can be derived so as to improve the VoIP platform\u27s revenue. Moreover, we also suggest several targets both in technical and economic view that the platform provider can strive in order to boost his/her market share. In addition, the case of Skype is discussed in this study and we also examine its current pricing strategy

Pneumocystis jiroveci Pneumonia in Patients with Non-Hodgkin's Lymphoma Receiving Chemotherapy Containing Rituximab

AbstractRituximab enhances treatment efficacy of B-lineage lymphoma by targeting CD20+ B-cells. Such target therapies may compromise the immune system and render patients susceptible to opportunistic infections. We report 2 cases of lymphoma complicated with Pneumocystis jiroveci (previously known as P. carinii) pneumonia (PCP) while being treated with rituximab-containing chemotherapy regimens. In both cases, PCP developed during the neutropenic period. With timely diagnosis and proper management, both were treated successfully. We searched the literature and found that such opportunistic infection occurred only infrequently in lymphoma patients, and it has not been reported in the large-scale clinical trials of rituximab. Such cases demonstrate the importance of taking PCP into diagnostic consideration in lymphoma patients receiving similar therapies

Small B cell lymphocytic lymphoma presenting as obstructive sleep apnea

BACKGROUND: Most lymphomas that involve the tonsil are large B cell lymphomas. Large B-cell lymphoma is a high grade malignancy which progresses rapidly. Tonsillar lymphoma usually presents as either a unilaterally enlarged palatine tonsil or as an ulcerative and fungating lesion over the tonsillar area. Small lymphocytic lymphomas (SLL) of the Waldeyer's ring are uncommon. CASE PRESENTATION: We report a 41-year-old male who presented with a ten-year history of snoring. Physical examination revealed smooth bilateral symmetrically enlarged tonsils without abnormal surface change or cervical lymphadenopathy. Palatal redundancy and a narrowed oropharyngeal airway were also noted. The respiratory disturbance index (RDI) was 66 per hour, and severe obstruction sleep apnea (OSA) was suspected. No B symptoms, sore throat, odynophagia or dysphagia was found. We performed uvulopalatopharyngoplasty (UPPP) and pathological examination revealed incidental small B-cell lymphocytic lymphoma (SLL). CONCLUSION: It is uncommon for lymphoma to initially present as OSA. SLL is an indolent malignancy and is not easy to detect in the early stage. We conclude that SLL may be a contributing factor of OSA in the present case